Optometry Semester 2

Microbiology and Parasitology, Optometry Notes, Optometry Semester 2

Bacterial Cell Structure and Classification

OPTOMETRY · SEMESTER 2 Bacterial Cell Structure and Classification Microbiology and Parasitology START READING NOTES Contents of This Topic Learning Objectives Definition of terms Definition of terms cont….. Characteristics of Prokaryotic Cells Characteristics of Prokaryotic Cells cont.. Bacteria parts and their functions Bacteria parts and their functions cont. Functions of Each Part of the Bacterial Cell Functions of Each Part of the Bacterial Cell cont.. Eukaryotic cell Characteristics of eukaryotic cell Characteristics of eukaryotic cell cont.. Main Distinguishing Features of Prokaryotic and Eukaryotic Cells Main Distinguishing Features of Prokaryotic and Eukaryotic Cells cont.. Major Similarities between Prokaryotes and Eukaryotes Bacteria Classification 1. Classification of Bacteria According to Morphology/Shape 1. Classification of Bacteria According to Morphology/Shape cont.… Bacteria shapes Bacilli bacteria in mass together 2. Classification of Bacteria basing on gram staining 3. Classification of Bacteria basing on spore forming 4. Classification of Bacteria basing on oxygen (air) requirement Basing biochemical reactions According to biochemical reactions cont.…. 6.Classification basing on flagella possession 7.Basing on nutritional requirements Classification of bacteria basing on pathogenicity Questions Bacteria Cell Structure and Classification Learning Objectives By the end of this session, students are expected to be able to: Define the terms bacteriology, prokaryotic cell, eukaryotic cell and bacteria Describe the characteristics of a prokaryotic cell Describe structure and functions of each part of a bacterial cell Compare prokaryotic cells and eukaryotic cells Classify bacteria according to various criteria Definition of terms Bacteriology: Is the Brach of microbiology which deals with the study of bacteria. Prokaryotic Cells Definition: Cells that lack a true nucleus and membrane-bound organelles. Structure: DNA floats freely in the cytoplasm (not enclosed in a nucleus). Have a cell membrane, cytoplasm, and ribosomes. Examples: Bacteria Definition of terms cont….. Eukaryotic Cells Definition: Cells that have a true nucleus and membrane-bound organelles. Structure: DNA is enclosed within a nucleus. Contains organelles like mitochondria, ER, Golgi apparatus, and lysosomes. More complex internal organization. Examples: Animals, plants, fungi, and protists. Size and Complexity: Larger and more complex. Definition of terms cont….. What Are Bacteria? Definition: Bacteria are microscopic, single-celled organisms with a prokaryotic cell structure, meaning they lack a true nucleus and membrane-bound organelles. Diversity: There are millions of different types of bacteria found all over the world—including in soil, water, air, and inside living organisms Characteristics of Prokaryotic Cells Prokaryotic nature/no true nucleus: Bacteria lack a true nucleus and membrane-bound organelles. Their DNA floats freely in the cytoplasm. Unicellular/single celled organisms: Each bacterium is a single celled, though some form colonies. Cell Wall made up of peptidoglycan: Most bacteria have a rigid cell wall made of peptidoglycan, which provides shape and protection. Characteristics of Prokaryotic Cells cont.. Posses different shapes: Common shapes include: Coccus (spherical) Bacillus (rod-shaped) Spirillum (spiral-shaped) Reproduction is by asexual reproduction: They reproduce asexually through binary fission, a process where one cell splits into two identical cells Characteristics of Prokaryotic Cells cont.. Metabolism: Bacteria can be autotrophic (making their own food) or heterotrophic (consuming organic material) and chemotrophs Motility: Some bacteria move using flagella, while others glide or twitch. Adaptability: Bacteria can survive extreme environments—hot springs, acidic lakes, deep-sea and vents. Ribosomes: They contain 70S ribosomes, which are smaller than those in eukaryotic cells. Pathogenicity: Some bacteria cause diseases in humans, animals, and plants, while others are beneficial (e.g., gut flora, nitrogen-fixing bacteria). Bacteria parts and their functions Structure Function Cell Wall Provides shape and protection; made of peptidoglycan in most bacteria. Cell Membrane Controls movement of substances in and out of the cell. Cytoplasm Jelly-like substance where cellular processes occur. Nucleoid Region containing the bacterial DNA (not enclosed in a nucleus). Bacteria parts and their functions cont. Nucleoid Region containing the bacterial DNA (not enclosed in a nucleus). Plasmid Small circular DNA molecules; often carry antibiotic resistance genes, uv resistance, and virulence Ribosomes (70S) Sites of protein synthesis. Flagella Tail-like structures used for movement. Pili (Fimbriae) Hair-like structures for attachment to surfaces or other cells. Bacteria parts and their functions cont. Capsule Slimy outer layer that protects against desiccation and immune attack. Inclusion Bodies Storage sites for nutrients or other substances. Endospore Dormant, tough structure formed by some bacteria to survive harsh conditions. Bacteria cell Diagram of Bacterial cell Functions of Each Part of the Bacterial Cell Cell component Description Functions Cell wall Is the outer most supporting layer which protects the internal structure of a cell Protection of internal structures (supporting layer) Gives shape to the cell Confers stability to osmotic pressure (mucopeptide toughens the cell wall) Role in division of bacterial Offers resistance to harmful effect of environment Functions of Each Part of the Bacterial Cell cont.. Capsule Is gelatinous secretion of bacteria which gets organised as a thick coat around cell wall Protection against deleterious agents (antibacterial agents) example lytic enzymes Contributes to the virulence of Flagella Are long contractile filamentous appendages They are organs of movements Functions of Each Part of the Bacterial Cell cont.. Pilli Are (Fimbriae) hair like filaments that extend from the cell surface. They are shorter and straighter than flagella They are organs of adhesion Facilitate transfer of genetic materials from one bacteria to another Cytoplasmic/ Plasma membrane Is a thin and elastic layer surrounding a cytoplasm. It is made of lipoproteins and phospholipids .Controls the movement of water, ions, nutrients and excretory substances in and out of the cell. Secrets extracellular hydrolytic enzymes Functions of Each Part of the Bacterial Cell cont.. Cytoplasm Is a viscous watery solution or soft gell containing a variety of organic and inorganic solutes Supports cellular structures like ribosome, nutrient granules, metabolites plasmids and nucleoid materials Ribosomes Are small granules and pack the whole cytoplasm. They are the sites for protein synthesis Functions of Each Part of the Bacterial Cell cont.. Nucleoid (site for DNA and RNA Is the area of the cytoplasm in which DNA and RNA are located To store genetic information Responsible for mutation of a bacteria Eukaryotic cell Eukaryotic Cells Definition: Cells that have a true nucleus and membrane-bound organelles. Structure: DNA is

Epidemiology and Biostatistics, Optometry Notes, Optometry Semester 2

Additional Study Notes: Screening Measures and Worked Data Examples

OPTOMETRY · SEMESTER 2 Additional Study Notes: Screening Measures and Worked Data Examples Epidemiology and Biostatistics Additional Study Notes — newly authored explanations and examples. These sections supplement the supplied course material. START READING NOTES Contents of This Topic Learning objectives Prevalence and incidence An original screening table Avoiding data errors Learning objectives Calculate prevalence and basic screening-test measures; identify their denominators; and distinguish a screening result from a confirmed diagnosis. Prevalence and incidence Prevalence describes existing cases in a defined population at a specified time or during a stated period. Cumulative incidence describes new cases during follow-up among people initially at risk. An incidence rate uses person-time in the denominator. Always state the population, condition definition and time frame. Original example: if 60 of 300 examined students have the defined condition on the survey date, sample prevalence is 60/300 = 20%. This estimate does not automatically describe all students in the district; the sampling process, participation and measurement method affect generalisability. An original screening table Hypothetical results for 1,000 people with a reference assessment: 90 true positives, 10 false negatives, 180 false positives and 720 true negatives. These counts are invented for calculation practice. Sensitivity = TP/(TP+FN) = 90/100 = 90%. Specificity = TN/(TN+FP) = 720/900 = 80%. Positive predictive value = TP/(TP+FP) = 90/270 ≈ 33.3%. Negative predictive value = TN/(TN+FN) = 720/730 ≈ 98.6%. The disease prevalence in this example is 100/1,000 = 10%. Despite high sensitivity, only about one-third of positive screens are true positives. Predictive values depend on the population prevalence as well as test performance. A positive screening result needs the appropriate confirmatory pathway. Avoiding data errors Keep raw observations, units and coding definitions. Use a distinct code for missing data rather than silently entering zero. Check impossible values, duplicate records and inconsistent eye or patient identifiers. Define whether an analysis is per person or per eye: two eyes from one person are not automatically independent observations. Report the sample size and denominator with every percentage. For a small or skewed dataset, examine the distribution before choosing summary measures. A median describes the middle ordered observation; a mean uses all values and is sensitive to extreme observations. Study References Source notes: Concepts of Biostatistics; Data Collection; Introduction to Epidemiology CDC: Evaluating Public Health Surveillance Systems — predictive value External references checked 13 September 2026. Worked numerical examples and teaching activities are original. ← PREVIOUS TOPICVIEW MODULE NOTESVIEW SEMESTER NOTESALL OPTOMETRY NOTES Need These Notes as PDF? Request a formatted copy for offline study, printing or revision. GET PDF NOTES ON WHATSAPP

Epidemiology and Biostatistics, Optometry Notes, Optometry Semester 2

Employ Knowledge Of Statistics In Collecting Health Data

OPTOMETRY · SEMESTER 2 Employ Knowledge Of Statistics In Collecting Health Data Epidemiology and Biostatistics START READING NOTES Contents of This Topic Related Tasks Definition Main tools used in statistical data collection 1. QUESTIONNAIRE Advantages of Questionnaire Disadvantages of Questionnaires Qualities of a good Questionnaire 2. INTERVIEW How to conduct interview Advantages of Interview Disadvantages of Interview 3. OBSERVATION (Observation checklist) Advantages of Observation Disadvantages of Observation 4. FOCUS GROUP DISCUSSIONS (FGDs) Advantages of FGDs Disadvantages of FGDs 4. CENSUS Disadvantages of Census METHODS OF DATA COLLECTION A. Primary data collection methods Sources of primary data B. Secondary data collection method Sources of secondary data Unpublished sources Factors influencing the choice of data collection method HOW TO DEVELOP DATA COLLECTION TOOLS STEPS IN DEVELOPING DATA COLLECTION TOOLS Principles in Using data collection tools EMPLOY KNOWLEDGE OF STATISTICS IN COLLECTING HEALTH DATA Related Tasks Define the term data collection. Identify tools used in statistical data collection Describe main methods of collecting statistical data Develop tools for data collection Use tools for data collection Definition DATA COLLECTION is the systematic process of gathering, measuring, and recording information from individuals, groups, observations, or sources for the purpose of analysis, interpretation and decision making. It is an important step in statistics, biostatistics, epidemiology, and research because the quality of collected data directly affects the accuracy and reliability of study findings. Main tools used in statistical data collection Questionnaires Interviews Observation checklists Focus group discussions (FGDs) Rating scales (E.g. Likert scale) Medical and Administration Records Tests and Examinations census 1. QUESTIONNAIRE Is a written set of questions answered by respondents. TYPES OF QUESTIONNAIRE Structured questionnaires- fixed responses E.g. Yes/No Semi-structured questionnaires- Both fixed and open-ended questions Unstructured questionnaires- Mostly open-ended questions Advantages of Questionnaire Can collect large amounts of data Cost effective Time-saving Standardization of responses Easy to analyze No interview bias Disadvantages of Questionnaires Low response rate Misinterpretation of questions Limited depth of information Incomplete or missing data Not suitable for illiterate population Risk of dishonest or biased response Qualities of a good Questionnaire Clear instruction Demographics Grammar Proper space for response Simple questions As per objectives Pilot study 2. INTERVIEW Is a data collection tool which involves direct verbal interaction between the researcher and participant (interviewer and interviewee) It consists of a set of pre-written questions that are asked by an interviewer and filled in by the interviewer called Interview Schedule TYPES OF INTERVIEW Structured interview- standardized set of pre-determined questions in a fixed order. Semi-structured interview- Uses a pre-prepared set of guiding questions but allows the interviewer to ask additional probing questions. Unstructured (informal) interview- An interviewer asks open-ended questions. How to conduct interview Conducted as per objectives Plan for time, duration, place, mode of recording Respect not to answer right of subject Simple and appropriate language Positive body language Advantages of Interview Provides in-depth information Clarification of questions is possible High response rate Suitable for all literacy levels Allows probing and follow up questions Allows better control over data collection process Disadvantages of Interview Time-consuming Expensive Interview bias Requires skilled personnel Possibility of response bias Limited anonymity (respondents may feel uncomfortable sharing sensitive or personal information) 3. OBSERVATION (Observation checklist) In this tool a research observe and record behaviors, events or condition using a checklist. TYPES OF OBSERVATION Overt- subjects are aware Covert- subjects are not aware Participant Non-participant Advantages of Observation Provide direct information Captures the real-life behavior Useful when subjects can not communicate Minimizes response bias Provides contextual information Useful for verifying other data sources Disadvantages of Observation Observer bias Time-Consuming Limited scope of data Hawthorne effect Expensive in some cases Ethical concerns (observing people without their knowledge may raise privacy and consent issues) 4. FOCUS GROUP DISCUSSIONS (FGDs) A small group discussion guided by a moderator to obtain opinions and perception. Number of participants Minimum- 6 participants Optimal range- 6-8 participants (most commonly used in qualitative health research) Maximum- 10-12participants Advantages of FGDs Generates rich qualitative data Encourage interaction among participants Efficient data collection method (large amount of information can be collected from several participants at the same time) Explores diverse perspectives Helps in identifying new idea or issues Useful for understanding social norms and behavior Cost effective compared to individual interview Disadvantages of FGDs Dominance by certain participants Lack of confidentiality Group pressure (conformity bias)- Individuals change their opinions, attitudes, or responses to match those of a group) Requires skilled moderator Logistical challenges 4. CENSUS It involves the complete enumeration of all members of a defined population at a specific point in time It aims to gather detailed information about demographic, social , and economic characteristics. Advantages of census No sampling bias High accuracy and reliability Detailed information Benchmark data Disadvantages of Census Very expensive Time consuming Not suitable for frequent studies METHODS OF DATA COLLECTION Statistical data collection methods are systematic approaches used to gather information for analysis, interpretation, and decision making in research, epidemiology, public health and biostatistics. These methods are broadly divided into, Primary data collection methods Secondary data collection methods A. Primary data collection methods Observation method Interview method Questionnaire method Experimental method Focus group discussion Measurement method Sources of primary data Direct observation Experiments Focus group discussion Interview Survey and field studies Measurements and tests Case studies B. Secondary data collection method Secondary data are data already collected by others for another purpose. Sources of secondary data Published sources Government reports Journals Census data WHO reports Books Unpublished sources Hospital records Institutional data base Research theses Factors influencing the choice of data collection method Research objectives Nature of data needed Available time Cost and resources Literacy level of participants Population size Accuracy required HOW TO DEVELOP DATA COLLECTION TOOLS This is the systemic process of designing instruments used to gather accurate, reliable, and relevant information for research, epidemiology, biostatistics and public health studies. Data collection tools should be carefully developed to ensure the quality of data collected. STEPS IN DEVELOPING DATA COLLECTION TOOLS There are four steps in developing data collection

Epidemiology and Biostatistics, Optometry Notes, Optometry Semester 2

Describe Concepts Of Epidemiology In Disease Prevention

OPTOMETRY · SEMESTER 2 Describe Concepts Of Epidemiology In Disease Prevention Epidemiology and Biostatistics START READING NOTES Contents of This Topic Learning Objectives Explain factors related to health and disease Epidemiology Definition of epidemiology Describe Concepts Of Epidemiology In Disease Prevention Study of the distribution (pattern of disease i.e. time, place, person). Definition of terms used in epidemiology Definition of terms cont… Definition of Health Describe natural history of disease Stages of Pathogenesis Factors in Pre-Pathogenesis Factors in Pathogenesis Outline key applications and achievements of epidemiology Achievements of epidemiology The determinants of health The determinants of health include; Key Points Key points cont… aims/Uses/Applications of epidemiology reference Describe the concepts of epidemiology in disease prevention Learning Objectives By the end of this session, students are expected to be able to: Define terms used in epidemiology Define health and disease Describe Natural History of disease Outline key applications and achievements of epidemiology Explain the determinants of health and disease -INTRODUCTION TO EPIDEMIOLOGY Explain factors related to health and disease Distinguish factors related to health and disease -INTRODUCTION TO EPIDEMIOLOGY Epidemiology The word epidemiology comes from the Greek words epi = meaning on or upon demos = meaning people logos = meaning the study of or doctrine Thus the word “epidemiology” simply means the study of what is happening to people -INTRODUCTION TO EPIDEMIOLOGY Definition of epidemiology As per perkins 1873 it is that branch of science which treats epidemics As per frost 1927 it is the science of mass phenomenon of infection disease. As per greenwood 1934 the study of any disease as a mass phenomena -INTRODUCTION TO EPIDEMIOLOGY Describe Concepts Of Epidemiology In Disease Prevention Epidemiology is often more concerned with the well-being of society as a whole, than with the well-being of individuals. In these definitions, three components are common. Study of the disease frequency(frequency of disease, disability or death and summarizing in the form of rates and ratios). -INTRODUCTION TO EPIDEMIOLOGY Study of the distribution (pattern of disease i.e. time, place, person). Study of determinants (underlying cause or risk factors). -INTRODUCTION TO EPIDEMIOLOGY Definition of epidemiology « The study of the distribution and determinants of health related states or events in specified populations and the application of this study to the control of health problems. -INTRODUCTION TO EPIDEMIOLOGY Definition of terms used in epidemiology Distribution is concerned with the frequency and pattern of health events in a population Distribution: What, who, when, and where Frequency: number, rates, and risk Quantify diseases to determine magnitude Patterns: time, place, and person -INTRODUCTION TO EPIDEMIOLOGY Definition of terms cont… Frequency: refers to the number of health events e.g. Number of cases of meningitis, Number of cases of diabetes in a population, Number of people with mental disorder in a population, Number of children under one year of age vaccinated for measles. Pattern of disease refers to the occurance of health related events or disease by time, place and person. -INTRODUCTION TO EPIDEMIOLOGY Definition of Health Health: A state of complete physical, mental, and social well-being and not merely the absence of disease or infirmity. (World Health Organization) Definition of Disease Disease: A disorder of structure or function in a human, especially one that produces specific symptoms or that affects a specific part. Definition of agent Is an microorganism/microbe that is cable of causing a disease -INTRODUCTION TO EPIDEMIOLOGY Describe natural history of disease Definition: Natural history of a disease the course of a disease over time, unaffected by human interventions. Pathogenesis: Step-by-step origination and development of a disease. -INTRODUCTION TO EPIDEMIOLOGY Stages of Pathogenesis Pre-Pathogenesis: Occurs before the onset of disease; interaction between host, agent, and environment. Pathogenesis: Interaction leads to discernible lesions or symptoms. Intervention can shorten or prevent this. Post-Pathogenesis: Residual effects persist; new diseases may arise from post-pathogenesis of others. Factors in Pre-Pathogenesis Host Factors: Age, sex, social class, personality, genetic makeup, etc. Agent Factors: Presence of an etiological factor necessary for disease. Risk Factors: Fixed (e.g., age) or modifiable (e.g., smoking). Environmental Factors: Climate, altitude, population density, sanitation, etc. Factors in Pathogenesis Host-Agent Interaction: Time between onset and discernible disease or symptoms. Outcome: May lead to recovery, disability, or death.Human Intervention can terminate or shorten this process. Outline key applications and achievements of epidemiology The applications of epidemiology include; Disease surveillance Disease investigation Risk analysis Design of prevention strategies Natural history Diagnostic testing -INTRODUCTION TO EPIDEMIOLOGY Achievements of epidemiology Community diagnosis Tools for data analysis Foundation for modern Public health Integration into various fields -INTRODUCTION TO EPIDEMIOLOGY The determinants of health Many factors combine together to affect the health of individuals and communities. Whether people are healthy or not, is determined by their circumstances and environment. -INTRODUCTION TO EPIDEMIOLOGY The determinants of health include; Income and social status Education Physical environment Social support networks Biology and genetic endowment Health services (availability and accessibility) Gender -INTRODUCTION TO EPIDEMIOLOGY Key Points As a discipline within public health, epidemiology includes the study of the frequency, patterns, and causes of health-related states or events in populations, and the application of the information gained to public health issues. In epidemiology, our “patient” is the public at large—the community—and in “treating” our patient we perform several tasks, including public health surveillance, disease investigation, analytic epidemiology, and evaluation. -INTRODUCTION TO EPIDEMIOLOGY Key points cont… Epidemiology provides us with a systematic approach for determining What, Who, Where, When, and Why/How. We use descriptive epidemiology to describe disease occurrence by person (Who), place (Where), and time (When). We use descriptive epidemiology to portray the characteristics and public health of a population or community. We use analytic epidemiology to sort out and quantify potential risk factors and causes (Why). -INTRODUCTION TO EPIDEMIOLOGY aims/Uses/Applications of epidemiology Describe the distribution of diseases and burden in a population Identification of etiological factors in pathogenesis Provide and analyze information for planning, implementation and evaluation of health status Study the natural history of disease -INTRODUCTION TO EPIDEMIOLOGY reference Bety R. K., & Jonathan A. C. S. (2003) Medical Statistics (2nd Ed.),

Epidemiology and Biostatistics, Optometry Notes, Optometry Semester 2

Concepts Of Biostatistics In Managing Health Data

OPTOMETRY · SEMESTER 2 Concepts Of Biostatistics In Managing Health Data Epidemiology and Biostatistics START READING NOTES Contents of This Topic Sub-Enabling Outcome a) Define terminologies used in biostatistics Key Concepts of Biostatistics in Health Data Management b) Data Organization and Classification c) Data Summarization (Descriptive Statistics) d) Data Analysis (Inferential Statistics) e) Interpretation of Results f) Data Presentation g) Decision-Making and Policy Formulation Summary Table b) Explain importance of biostatistics 2. Helps in Health Research and Innovation 3. Enables Disease Surveillance and Control 4. Assists in Planning and Policy Formulation 5. Facilitates Evaluation of Health Programs 6. Improves Quality of Health Data 7. Helps Understand Risk Factors for Diseases 8. Aids in Predicting Health Trends 9. Enhances Communication of Scientific Findings 10. Promotes Rational Use of Resources c) Explain importance of data stratification Importance of Data Stratification b) Helps Identify Hidden Trends and Patterns c) Supports Targeted Interventions d) Enhances Equity and Resource Allocation e) Facilitates Monitoring and Evaluation f) Reduces Bias and Misleading Conclusions g) Supports Health Research and Policy Development h) Improves Quality Improvement in Health Facilities d) Explain different types of biostatistical data Main Types of Biostatistical Data i. Nominal Data ii. Ordinal Data B. Quantitative (Numerical) Data Examples: ii. Continuous Data 3. Summary Table Importance of Knowing Data Types In Summary References….. CONCEPTS OF BIOSTATISTICS IN MANAGING HEALTH DATA Sub-Enabling Outcome 1.1.1 Describe concepts of biostatistics in managing health data Related Tasks a) Define terminologies used in biostatistics b) Explain importance of biostatistics c) Explain importance of data stratification d) Explain different types of biostatistical data a) Define terminologies used in biostatistics Definition of Biostatistics Biostatistics is the branch of statistics that applies statistical methods to biological, medical, and health-related research. It involves collecting, analyzing, interpreting, and presenting health data to support evidence-based decision-making in healthcare. Key Concepts of Biostatistics in Health Data Management a) Data Collection This involves gathering health information from sources such as surveys, hospital records, laboratory results, or public health surveillance systems. Biostatistics provides methods for designing valid sampling techniques and data collection tools to ensure accuracy and representativeness. Example: Selecting a random sample of patients to estimate disease prevalence in a community. b) Data Organization and Classification Health data are organized into categories or groups for easier analysis. Data may be quantitative (numerical) or qualitative (categorical). Biostatistics helps classify data into nominal, ordinal, interval, or ratio scales depending on the type of variable. Example: Classifying patients by blood group (nominal) or by disease severity (ordinal). c) Data Summarization (Descriptive Statistics) Biostatistics uses measures such as mean, median, mode, standard deviation, and range to summarize and describe data patterns. Graphical tools like bar charts, histograms, and pie charts help visualize the distribution of health data. Example: Calculating the average age of malaria patients or showing TB cases by region in a bar chart. d) Data Analysis (Inferential Statistics) Involves drawing conclusions or inferences about a population from a sample. Uses techniques such as hypothesis testing, correlation, regression, t-tests, and chi-square tests. Helps identify associations and causes in health outcomes. Example: Testing whether smoking is significantly associated with lung cancer incidence. e) Interpretation of Results Statistical findings are interpreted in the context of health and medical knowledge. Biostatistics helps health professionals understand whether observed patterns are due to chance or real associations. Example: Interpreting that an increase in vaccination coverage is statistically linked to reduced measles outbreaks. f) Data Presentation Biostatistics emphasizes clear presentation of results through tables, graphs, charts, and reports. Proper visualization aids communication of findings to policymakers, researchers, and the public. Example: Presenting maternal mortality trends in a line graph to guide national health planning. g) Decision-Making and Policy Formulation Statistical evidence guides public health decisions, program evaluation, and policy development. Enables assessment of intervention effectiveness, disease trends, and health system performance. Example: Using biostatistical analysis to determine whether a malaria control program effectively reduced infection rates. Summary Table Concept Description Example Data Collection Gathering health data Hospital records, surveys Data Organization Classifying data Grouping patients by diagnosis Descriptive Statistics Summarizing data Mean, median, charts Inferential Statistics Drawing conclusions Hypothesis testing Interpretation Understanding meaning Relating statistics to health outcomes Data Presentation Displaying results Graphs and tables Decision-Making Using evidence for action Health policy formulation b) Explain importance of biostatistics Importance of Biostatistics 1. Supports Evidence-Based Decision Making Biostatistics provides the numerical foundation for making informed decisions in medicine and public health. Through statistical analysis, health professionals can identify what interventions work best, evaluate treatment outcomes, and make policies based on scientific evidence rather than assumptions. Example: Determining the effectiveness of a new vaccine by comparing infection rates between vaccinated and unvaccinated groups. 2. Helps in Health Research and Innovation Biostatistics is essential in designing, conducting, and analyzing medical and public health research. It guides sample selection, data collection methods, and the correct use of statistical tests to ensure research findings are valid and reliable. Example: In clinical trials, biostatistics helps determine whether a new drug is significantly better than existing treatments. 3. Enables Disease Surveillance and Control Biostatistics helps in monitoring patterns and trends of diseases in populations. By analyzing data over time, health authorities can detect outbreaks, measure disease burden, and evaluate control measures. Example: Using statistical trends to track and control the spread of malaria or COVID-19. 4. Assists in Planning and Policy Formulation Health planners use biostatistics to forecast future health needs, allocate resources efficiently, and set realistic health targets. It ensures that public health policies are guided by quantitative evidence. Example: Using birth and death rate data to plan maternal and child health services. 5. Facilitates Evaluation of Health Programs Biostatistics provides tools for monitoring and evaluating the impact and cost-effectiveness of health programs. This helps in improving performance and ensuring accountability. Example: Assessing whether a nutrition program reduces malnutrition rates in children under five. 6. Improves Quality of Health Data Statistical principles help ensure accuracy, reliability, and validity of collected health information. This reduces errors and enhances confidence in conclusions drawn from the

Epidemiology and Biostatistics, Optometry Notes, Optometry Semester 2

Basic statistical method in compiling health data

OPTOMETRY · SEMESTER 2 Basic statistical method in compiling health data Epidemiology and Biostatistics START READING NOTES Contents of This Topic Learning Objectives Methods of statistical Definition of a Variable. Types of Variables. Quantitative (Numerical) Variables Continuous variables take any value within meaningful extremes, can take decimals, for example: Levels of Measurement Example 1: Gender (male or female) is a common nominal variable used in epidemiologic studies. Ordinal Measurement Interval Measurement Basic statistical method in compiling health data Differences Between Nominal, Ordinal, Interval and Ratio Measurements Frequency and Relative Frequency Distribution – 1 Frequency and Relative Frequency Distribution – 2 Frequency and Relative Frequency Distribution – 4 Note: A frequency distribution can be displayed as a table, a bar chart, a histogram, or a frequency polygon. Use of Tallies in Making Frequency Distribution – 1 Use of Tallies in Making Frequency Distribution – 2 Use of Tallies in Making Frequency Distribution – 3 Sputum Examination for Possible TB Infection Sample Raw Data From the above data we can summarize as follows Can We Summarize it Further? A better summarization! Use of Diagrams Pie Charts Example: 2017 TTCIH Students’ Enrollment Data Bar Chart – 1 Bar Chart – 2 Example: Why not use a pie chart in the previous table? Two-Way Tables – 1 Two-Way Tables – 2 Example Pulmonary Tuberculosis by HIV Status Two-Way Table – 3 Take Home! Basic statistical method in compiling health data. Learning Objectives By the end of this session, students are expected to be able to: Explain methods of statistical data categorization Identify levels of statistical data measurement Compile health data using appropriate statistical methods Methods of statistical data categorization Data: The raw material of statistics. Data generally consists of numbers of measurement or counting of a population sample. The methods of summarizing data (methods of descriptive statistics) vary with different types of data that are generated from different types of variables. Definition of a Variable. Variable: A term for a characteristic that is different in different members of a population or sample, such as height. This measurement is not constant, so therefore it is variable. Variables can be qualitative or quantitative, continuous or discrete. Types of Variables. There two types of variables: Qualitative (categorical) variables Quantitative (numerical) variables Qualitative (Categorical) Variables Qualitative variables do not take numerical values (e.g. gender: male/female). Outcome of disease (recovery, chronic illness, death) Hair color (black, blonde) Marital status (single, married, widowed, separate, divorced) Quantitative (Numerical) Variables Quantitative variables take numerical values, for example: Age (years): 10, 19, 45, 60 Height (cms):140, 50.6, 200 Parity: 0, 1, 2, 3, 4, 5, 6, 10. Quantitative variables are of two types: continuous and discrete Continuous variables take any value within meaningful extremes, can take decimals, for example: Height (cm): 159, 25, 160.35 Weight (kg): 71.12, 80.56 Exact age like 21 yrs 6 months and 4 days Discrete variables take only fixed values, in most cases whole numbers, for example: Parity: 0, 1, 2, 3, 4, 5, 6, 10 Levels of Measurement Variables are measured on different levels/scales The term ‘measurement’ is used here in a broad sense These are nominal, ordinal, and ratio measurements Nominal Measurement The nominal scale classifies persons or things based on a qualitative assessment of the characteristic being assessed. It neither includes information on quantity or amount nor does it indicate ‘more than’ or ‘less than’ Example 1: Gender (male or female) is a common nominal variable used in epidemiologic studies. Other examples: These used for identifying various categories that make up a given variable e.g. Religion: 1 = Muslim, 2 = Christian, 3 = Ordinal Measurement The ordinal scale also classifies persons or things based on the characteristic being assessed but does indicate ‘more than’ or ‘less than’. In this sense, it provides more information than the nominal scale. Example: Rating students’ performance as being poor, average, good, or excellent indicates how well students perform and provides a basis for comparison. However, it does not indicate how much better an excellent performance is compared to a good one. Interval Measurement The interval scale has the same characteristics of the ordinal scale – classifying persons or things based on the characteristic assessed and indicating more than or less than – but the interval scale indicates how much more than or less than. The interval scale does not indicate a true zero point, meaning that there cannot be an absence of a characteristic being measured. Basic statistical method in compiling health data Example: Temperature is an interval in that different values can tell you how much more or less. However, there is no true zero point. The value of zero in temperature does not indicate absence of temperature. Ratio Measurement The ratio scale includes all the characteristics of the interval scale but does indicate a true zero point. Example: Height and weight measurements indicate how much more or less, but also have a true zero point. A weight of zero indicates an absence of weight. Differences Between Nominal, Ordinal, Interval and Ratio Measurements Nominal Ordinal Interval Ratio Classifies persons or things based on a qualitative assessment Similar or dissimilar but not more or less Can be numeric but there is no implication of more or less Classifies persons or things based on a qualitative assessment More or less but not how much more or less Indicates how much more or less Does not contain a true zero point Cannot create meaningful ratios of these two numbers Includes all the characteristics of the interval scale, but contains a true zero point. Descriptive Methods for Qualitative Data Frequency and Relative Frequency Distribution – 1 Frequency distribution A presentation of the number of times (or the frequency) that each value (or group of values) occurs in the study population. Frequency distribution helps to give a picture of the shape of the distribution of the data. Frequency and Relative Frequency Distribution – 2 Unimodal data: Data that only has one peak. Bimodal data: Data that has two peaks. Multimodal data: Data

Epidemiology and Biostatistics, Optometry Notes, Optometry Semester 2

Apply Biostatistical Methods In Analyzing Health Data

OPTOMETRY · SEMESTER 2 Apply Biostatistical Methods In Analyzing Health Data Epidemiology and Biostatistics START READING NOTES Contents of This Topic APPLY BIOSTATISTICAL METHODS IN ANALYZING HEALTH DATA Learning tasks Definitions Data to be analyzed Methods for data analysis Data entry Data cleaning Data summarization Tools and applications for data analysis References APPLY BIOSTATISTICAL METHODS IN ANALYZING HEALTH DATA 1 Learning tasks At the end of this session, students are expected to be able to: Define data analysis Identify data to be analyzed Identify methods for data analysis Describe data entry process Explain data cleaning Explain data summarization List tools for data analysis Analyze health data 2 Definitions Data Analysis Is the systematic process of inspecting, cleaning, transforming, and modeling raw data to discover useful information, identify patterns, and support decision-making. 3 Data to be analyzed Qualitative Data: Non-numerical data from sources like interviews, open-ended survey questions, and observations Quantitative Data: Numerical data that represents quantities or measurements, such as sales figures, age, or height. 4 Methods for data analysis Data analysis has four main methods or techniques. Descriptive; Summarizes historical data to show what has happened by looking for causes and correlations. Predictive; uses historical data and models to forecast what is likely to happen in future. Diagnostic; Examines data to understand why something happened by looking for causes and correlations. Prescriptive; Recommends specific actions to be taken based on the predictions. 5 Data entry This is the manual or automated process of inputting or transferring data from physical or digital sources into an electronic format for an organization. 6 Data cleaning Is the process of finding and correcting errors, inconsistencies, and inaccuracies in a dataset to improve its quality. The goal is to ensure the data is reliable, complete, and consistent before analysis. 7 Data summarization Is the process of reducing large datasets into a more manageable and understandable form. This helps to highlight key aspects of data, such as patterns and trends without losing critical information. Techniques for summarization include calculating measures of central tendency(mean, median) and creating visual summaries like charts and graphs. 8 Tools and applications for data analysis Microsoft excel Stata R SPSS Python 9 References Kothar, C.R. (2004). Research Methodology: Methods and Techniques (2nd ed.). India: New Age International (P) Limited 10 ← PREVIOUS TOPICNEXT TOPIC →VIEW MODULE NOTESVIEW SEMESTER NOTESALL OPTOMETRY NOTES Need These Notes as PDF? Request a formatted copy for offline study, printing or revision. GET PDF NOTES ON WHATSAPP

Ocular Anatomy and Physiology, Optometry Notes, Optometry Semester 2

The Uveal Tract

OPTOMETRY · SEMESTER 2 The Uveal Tract Ocular Anatomy and Physiology START READING NOTES Contents of This Topic The Uveal Tract THE IRIS The Uveal Tract CHAPTER 9. THE UVEAL TRACT THE FOLLOWING TOPICS WILL BE COVERED BY THE END OF THIS CHAPTER: DEFINITION AND STRUCTURE OF THE UVEA THE IRIS THE CILIARY BODY THE CHOROID SOME DISORDERS AFFECTING THE UVEA A RWONS 1. DEFINITION AND STRUCTURE. The uvea is the vascular middle layer of the eye ball. When the outer layer , the sclera ,is removed the eye ball appears like a black grape hanging on its stalk( the optic nerve), hence the name. The uvea is made up of three structures: The iris. The ciliary body. The choroid The is no clear demarcation between these three parts, they are continuous with each other , lining the sclera from the anterior opening to the posterior aperture for the optic nerve. 2. THE IRIS. This is the most anterior part of the uvea, measuring about 12mm in diameter.. The iris is a thin, circular structure located anterior to the lens, often compared to a diaphragm of an optical ‘system. The center aperture It is a thin, contractile, SdoUghnUt/shaped” structure that is found in the anterior segment of the eye between the cornea and the lens. It in turn divides the anterior segment into anterior and posterior chambers. The anterior chamber is the space between the cornea and the iris, while the posterior chamber is the space between the iris and the lens. This division of the anterior segment is important for the Cataract/surgeons!) 53 The central opening of the “doughnut” is called the pupil. By varying the size of the pupil, the iris muscles ( sphincter and dilator) , control the amount of light entering the eye. All light that enters the eye, passes through the pupil. The aqueous humour , formed by the ciliary processes in the posterior chamber , circulates through the pupil into the anterior chamber. The iris is made up of : connective'tissue;muscles)/pigmented|cells (melanocytes), nerves, blood vessels. The colour of the iris varies from one individual to another, depending on the amount of pigment contained by the melanocytes. 2.1. Surface anatomy of the iris. a. The anterior surface. The anterior surface of the iris contains crypts and crevices in contact with the aqueous in the anterior chamber. The aqueous humour thus has direct communication with the tissue spaces of the iris. The center is the pupil, a black aperture with a varying diameteffrom=8 mm. The pupil appears black because the interior of the eye is dark. The anterior surface is divided into: e acentral, pupillary zone and e aperipheral , ciliary zone. The iris is thickest at the demarcation zone between the pupillary and the ciliary zones called collarette, which lies about 2mm from the pupillary zone. At the pupillary margin , a darker zone is seen surrounding the pupil. This is the so called pupillary ruff, representing the posterior pigmented layer of the iris curving around the pupillary margin. 54 b. The posterior surface. The posterior surface of the iris is markedly pigmented and shows a number of contraction folds. 2.2. Microscopic anatomy of the iris. The iris consists of two layers: a. the stroma; b. the pigmented epithelial layers; a. The iris stroma. The stroma devoid of epithelium, represents the anterior border of the iris. Embryologically itforiginates frommesenchymey) It is composed of a highly vascular connective tissue containing collagen fibres, fibroblasts, melanocytes, nerve fibres and the smooth muscles that control the pupillary movements (the sphincter and the dilator pupillae) Blood vessels form the bulk of the iris stroma. Their course is mostly radial, arising from the major arterial circle passing towards the centre. The major arterial circle is located in the ciliary body, not the iris. At the level of the collarette , anastomoses occur between arteries and veins, to form the minor vascular circle , which is often incomplete. The sphincter pupillae muscle is an 1mm wide circular band of smooth muscle fibers, located in the posterior stroma near the pupillary margin. Its innervation is by parasympathetic fibres fromthe Edinger Westphal fiiclelis of cranial/nerve lll;ithese fibres synapse in the ciliary ganglion and are distributed via the short posterior ciliary nerves to the sphincter muscle. When the sphincter pupillae contracts , the pupil constricts ( miosis ). The dilator pupillae is made up by myorpithelial cells that extend from the iris root to the sphincter pupillae, lying parallel and anterior to the posterior pigmented epithelium. The nerve supply is from the sympathetic postganglionic fibres via the long ciliary nerves. When the dilator muscle contracts , the pupil enlarges ( mydriasis ). 55 b. The pigmented epithelial layers. There are 2 pigmented layers, the anterior and the posterior pigmented layer. Embryologically derived from the neuroectoderm of the optic cup, the cells of the two layers are apposed to each other apex to apex. Between lies a potential space that can, under certain circumstances, fill _ with fluid and become real space. The anterior epithelial layer , only slightly pigmented, lies in contact with the iris stroma and is closely associated with the myoepithelial cells of the dilator pupillae muscle. It is continuous withithejouten layer of the ciliary epithelium: The posterior epithelial layer , facing the posterior chamber, is made of cells densely packed with melanin. Anteriorly it extends to the pupillary ruff while posteriorly is continous with the inner layer of the ciliary epithelium. Anterior chamber angle Trabecular meshwork Ciliary zone Pupillary zone Schlemm's canal SOS Collarette [ — Pupil frill Pupillary 27 margin Anterior border Iris root layer Sphincter papillae __ Stroma with blood vessels and nerves Anterior epithelium— radial myopepithelial dilator papillae muscle Ciliary process Posterior epithelium pigmented epithelium Fig. 9.1. Diagram of iris and ciliary body anatomy. 56 2. THE CILIARY BODY. The ciliary body is aring shaped structuréthat bridges the iris'and! choroid. It is 6mm wide extending from the scleral spur (anteriorly ) to the ora serrata of the retina

Optometry Notes, Optometry Semester 2, Physical and Geometric Optics

Refraction

OPTOMETRY · SEMESTER 2 Refraction Physical and Geometric Optics START READING NOTES Contents of This Topic Refraction WHAT IS REFRACTION? REFRACTING MATERIALS THE REFRACTIVE INDEX AIR OTHER MEDIUM THE REFRACTIVE INDEX VARIES WITH WAVELENGTH REAL AND APPARENT DEPTH TOTAL INTERNAL REFLECTION USES OF TOTAL INTERNAL REFLECTION WHITE LIGHT IS POLYCHROMATIC DISPERSION THE FOLLOWING DERIVATION IS NOT FOR EXAMINATION PURPOSES. COLOUR SELECTIVE TRANSMISSION PRIMARY, SECONDARY & COMPLEMENTARY COLOURS Red 700 – 635 PIGMENTS, PAINTING AND PRINTING OPTICAL PATH LENGTH REFRACTION AT CURVED SURFACES = ̶ 5.88 D = ̶ 6.46 D Refraction REFRACTION CHAPTER CONTENTS REFRACTING MATERIALS …………………………………………………………………………………………………………………………… 0 WHAT IS REFRACTION?………………………………………………………………………………………………………………………………. 0 THE REFRACTIVE INDEX …………………………………………………………………………………………………………………………….. 1 THE REFRACTIVE INDEX VARIES WITH WAVELENGTH ……………………………………………………………………………….. 2 REFRACTION AT PLANE SURFACES……………………………………………………………………………………………………………. 2 REAL AND APPARENT DEPTH……………………………………………………………………………………………………………………… 3 TOTAL INTERNAL REFLECTION…………………………………………………………………………………………………………………… 4 USES OF TOTAL INTERNAL REFLECTION……………………………………………………………………………………………………. 5 WHITE LIGHT IS POLYCHROMATIC ……………………………………………………………………………………………………………… 6 DISPERSION ……………………………………………………………………………………………………………………………………………….. 8 COLOUR…………………………………………………………………………………………………………………………………………………….12 OPTICAL PATH LENGTH……………………………………………………………………………………………………………………………..15 REFRACTION AT CURVED SURFACES ……………………………………………………………………………………………………….15 LENS CLOCK II……………………………………………………………………………………………………………………………………………16Refraction WHAT IS REFRACTION? When a ray of light in air is incident on the surface of a transparent medium such as glass, some of it is reflected, whilst the remainder is transmitted. The larger the angle of incidence is, the larger the amount of light that is reflected. No medium is perfectly transparent and some absorption of light always occurs, the energy being converted to heat. This latter effect will be ignored. The direction of the ray inside the medium is different to that of the incident ray unless the incident ray is normal (perpendicular) to the surface. The transmitted ray is bent as it crosses the surface between one medium and another. This change of direction of the ray at the surface is called refraction. Figure 3.1: Refraction at the air/water and water/air interfaces The preceding diagrams show several important aspects of refraction. When a light beam goes from air into water along the normal to the surface between them, it simply continues along the same path. When it enters the water (an optically more dense medium) at any other angle, it is bent towards the normal. The paths are reversible; thus a light beam emerging from the water (into the optically less dense air) is bent away from the normal as it enters the air. This effect gives rise to the phenomenon of the apparent depths of objects. REFRACTING MATERIALS Common refracting materials are glass, (in particular high-grade optical quality glass), quartz, and a variety of plastics. These have been chosen not only for their effect on the direction of light rays passing through them, but also for their transparency, homogeneity, and their resistance to atmospheric corrosion. Optical glass is commonly used in the manufacture of prisms and lenses. Two main types of optical glass are available: these are crown and flint. The former is a compound of silica (sand, SiO2) and salts of sodium and potassium. In addition, small quantities of other materials such as barium and zinc oxides may be present. Flint glasses, in addition to the constituents above, contain oxides of lead and are denser than crown glasses. Certain plastics materials are now increasingly being used for ophthalmic lenses. In this category is the thermosetting material allyl diglycol carbonate, commonly known as CR-39 (the CR standing for Columbia Resin). These plastics start as linear polymer chains that get cross-linked permanently during molding. Therefore they cannot be remolded. Polyethylene, polystyrene, polyvinyl chloride and polytetrafluoroethylene (PTFE) are examples of thermoplastic materials. These plastics do not undergo any chemical change during the molding process and can therefore be remolded several times without changing their properties. AIR WATER AIR WATERRefraction THE REFRACTIVE INDEX Refraction occurs because light travels at different speeds in different media. We have previously noted that the speed of light in vacuum, c, equals 3 x 108 m/s, which is the maximum speed at which light travels. (We will assume that the light travels with the same speed in air.) In a material medium, the speed of the light, v, is less. The ratio of these speeds is the refractive index (n) of the medium. c n = v Since v is never greater than c, the index of refraction (which is a dimensionless number) is never less than 1. The index of refraction is sometimes called a measure of the optical density of the material. Materials with larger indices of refraction are said to be optically denser. The previous statements about the direction in which light rays are bent in passing into a different medium can now be restated in terms of optical density. In order to account for the light slowing down as it does, consider the accompanying figure which represents a beam of light entering a piece of glass from the left. Once inside the glass, the light may encounter an electron bound to an atom, indicated as point A in the figure. Let us assume that light is absorbed by the atom, which causes the electron to oscillate. The oscillating electron then acts as an antenna and radiates the beam of light toward an atom at point B, where the light is again absorbed by an atom at that point. (We need not consider the details of these absorptions and emissions.) For now, it is sufficient to think of the process as one in which the light passes from one atom to another through the glass. (The situation is somewhat analogous to a relay race in which a baton is passed between runners on the same team.) Although light travels from one atom to another with a speed of 3 x 108 m/s, the processes of absorption and emission of light by the atoms take time. Enough time is required, in fact, to lower the speed of the light in the medium. Once the light emerges into the air again, the absorptions and the emissions cease and its speed returns to the original value. Figure 3.2: A beam of light entering a piece of glass The frequency of a light wave is determined by its

Optometry Notes, Optometry Semester 2, Physical and Geometric Optics

Vergence

OPTOMETRY · SEMESTER 2 Vergence Physical and Geometric Optics START READING NOTES Contents of This Topic Vergence DEFINITION SIGN CONVENTION AND UNITS CALCULATING VERGENCE CURVATURE OF WAVEFRONTS EFFECTIVITY APERTURE, RADIUS OF CURVATURE AND SAGITTA LENS CLOCK I Vergence VERGENCE CHAPTER CONTENTS DEFINITION…………………………………………………………………………………………………………………………………………………. 1 SIGN CONVENTION AND UNITS…………………………………………………………………………………………………………………… 2 CALCULATING VERGENCE………………………………………………………………………………………………………………………….. 3 CURVATURE OF WAVEFRONTS ………………………………………………………………………………………………………………….. 4 EFFECTIVITY ………………………………………………………………………………………………………………………………………………. 5 APERTURE, RADIUS OF CURVATURE AND SAGITTA …………………………………………………………………………………… 7 LENS CLOCK I……………………………………………………………………………………………………………………………………………… 8 DEFINITION Much of the work in geometrical optics is concerned with the convergence and divergence of pencils of light rays. In fact, the main purpose of spectacle lenses is to alter the extent of convergence or divergence of light rays before they enter the eye. The convergence or divergence of a pencil of light rays may be expressed by the general term vergence. The vergence at a particular point in a pencil of rays travelling in air is the reciprocal of the distance from the point to the source or the focus. Clearly, we will be dealing with a source in the case of a diverging pencil and a focus in the case of a converging pencil. From the definition, it follows that the closer the point in question is to the source (or focus), the larger the vergence, and vice versa.Vergence The definition of vergence stated above does not distinguish between those points which are situated in converging pencils of rays and those points which are situated in diverging pencils. In order to be able to distinguish between diverging and converging pencils, when studying the effects of optical components such as lenses, a sign convention must be employed. A sign convention is a set of definite rules such that the value of any distance measured on an optical diagram may be given a positive or a negative sign, corresponding to convergence and divergence respectively. SIGN CONVENTION AND UNITS The sign convention for vergence is as follows. 1. In optical diagrams, light is assumed to travel from the left to the right in a positive direction. If the distance from the point in question to the source or focus is measured in the same direction as that in which the rays of light are directed, the numerical value of the distance is given a positive sign (+). 2. If the distance from the point in question to the source or focus is measured in the opposite direction to that in which the light is travelling, the magnitude of the distance is given a negative sign (−). Refer to the below figures. The distance from the point D to the source is measured in the opposite direction to the direction in which the light is travelling and we must apply a minus sign to the distance d. Hence, the vergence at D (= 1/d) will be a negative value. Figure 2.1: Diverging pencil of rays. The distance d is measured from the point to the source, hence from right to left leading to a negative value. However, the distance from the point C to the focus is measured in the same direction as the direction in which the light is traveling and the value of the distance cis assigned a plus sign. Therefore, the vergence at C (= 1/c) will be a positive value. Figure 2.2: The distance c is measured from the point to the focus, from left to right, leading to a positive value.Vergence These rules result in the important conclusion that at any point in a converging pencil of rays the value of the vergence of the light is positive, and at any point in a diverging pencil of rays the value of the vergence of the light is negative. It also follows that at any point in a parallel pencil of rays, for which the source or the focus may be considered to be at infinity, the vergence will be derived as follows: 1 vergence = = 0 ±∞ That is, at any point in a parallel pencil of rays, the value of the vergence of the light is zero. If the distance from a point in a pencil to the source or focus is expressed in metres, then the value of the vergence at that point is expressed in dioptres. We can define one dioptre, symbol 1 D, as being the magnitude of the vergence in a pencil of rays in air, at a point one metre from the source or the focus. CALCULATING VERGENCE Figure 2.3: a) Diverging pencil of rays b) Converging pencil of rays Refer to the previous diagrams of which (a) shows a diverging pencil and (b) shows a converging pencil of rays. The point from which the diverging pencil of rays actually originates will now be referred to as an object. In optics, the distance from a point such as A to an object is represented by the symbol l. Thus the distance from A to the object = l where l is measured in metres. The vergence at A is 1/ l and this is given the symbol L (dioptres). 1 L(dioptres) = l (metres) The point through which all the converging rays pass will be referred to as an image. We will represent the distance from a point such as B to an image by l as well. Care must be taken to apply the sign convention in order to find the correct sign for the vergence. The vergence at B will then also be given by the above equation. For any optical medium with an index of refraction n, the vergence of the light travelling through the medium is given l n L =Vergence It is worth emphasizing that the dioptre unit is really the reciprocal metre (m-1 ). The dioptre is merely a unit of convenience which is easier to say than ‘reciprocal metre’, but when considering units in some equations it will be necessary to think in terms of reciprocal metres. The name dioptre was chosen from dioptrics, the name given to the branch

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