Reflection of Light from Curved Mirrors

Difference between Concave atid Convex Mirrors

Concave mirror is a spherical mirror whose reflecting surface is curved inwards. A Good

example is the driving mimor of a car

General demonstrations of convex and concave mirrors (curved mirrors The Terms Principle, Axis, Pole, Principle Focus and Radius of Curvature as

Applied to Curved Mirrors

Terms used in studying curved mirrors B

• Centre of curvature (C):the centre of the sphere of which a mirror is a part of
• Radius of curvature (R): the radius of sphere of which a mirror sa part of

. Pole (P): the central point of the reflecting surface of spherical mirror (curved or convex miro), oD *

• c \

Printipal axis

• Prineipal focus (F):the point o the principal axis where light rays tend to intersect. This
• Prineipal axisihe straight ine joining ihe centre of curvature (C) and the pale ().
• Principal focus (Fsthe point onthe principal axis where light rays tnd to intersect. This

point is between centre of curvature and the pole The Images Formed by a Curved Mirror Case (1) When a beam of light parallel and very close to the prineipal ais, CL, is reflected fiom a coneave mirror, it converges to a point, F, on the prineipal axis called the principal focus.

u ooo

L P K c

Ny ie Case 2 When a ray passes through the principal focus, F it is reflected parallel to the principal axis. a -——— 55 c \ Se \ es Case 3 2s Ip Note: Concave mirrors have a real focus because light passes through the focus, The formation of images by concave mirror tends to change as the postion of object changes Case 1; Image (I) formed by a concave mirror when the object is beyond C.

a as a

€ F P Foe

Properties of images formed

1 The image is between C and F 2 The image is smaller than the object

• The image is inverted (upside down)

4, The image is real Case 2. The object is placed at C wa é # {2 c \ i \ “Sky 2 The image is large than object

• The image is formed beyond C

a 8 The image is inverted (upside down) ts. [Las c F > re \ Se \ Sh

• The image is Real
• rf

a 4 ‘The image is large than the object

Formation of images in a convex mirror

Obviously.there isonly one kind of image formed when an object is placed at any position.

Properties of image formed by convex mirror

1 the image is virtual 2 theimage is upright

• The image is smaller than object (diminished)
• ‘The image is formed behind the mirror

Example 1

An object 2cm long is erected 86m infront of a concave mirror of radius of curvature 10cm. By using a scale drawing, determine the position, size and nature of image formed Data given

• Height of object, Ho ~ 2em
• Object distance, U= Bem
• Radius of curvature, r= 10cm
• Focal length, =Rem
• Choose suitable scale
• Say tem represents Sem

From this seale then

• Height of object, Ho = 2em
• Object distance, U= 2em
• Focal length, F=2.Sem

Thas,

Image Height, Hi-Y

The Focal Length of a Concaye Mirror Determine practically the focal length of a concave mirror Focal length (f) is the distance between the principal focus and the pole yi ih — Ee Ki Convex and Concave Mirrors in Daily Life Use Convex and concave mirrors in daily life Curved mirrors are used as: 1 Driving mirrors

• Shaving mirrors
• Reflectors

Why is convex mirror used as driving mirror? Why concave mirror used as shaving mirror?

Refraction of Light

The Concept of Refraction of Light

Explain the concept of refraction of light because the spood of light tends fo change when travelling from one medium to another Ai class Va aw ‘The Angle of Incidence and Angle of Refraction The angle of incidence (iis the angle between the incident ray of light and the normal at the The angle of Refraction (r)is the angle between the refracted ray and the normal at the point of incidence

The Laws of Refraction

State the laws of refraction First law of refraction ryt Second law of refraction Second Law of reffaction states that “when a light ray passes from one medium into another medium, the angle of incidence (i) and corresponding angle of reftaction( r) are such that the ratio of sine of the angle of incidence to the sine of the angle of refraction (sini/sine) is a constant value called the refractive index.” Note: The Second Law of Refraction is called Snell's Law in honour of a Dutch scientist named

Snell (1591 — 1626) who first deseribed it ‘The Refraction Index of a Material Determine the refraciton index of a marerial Reffactive index (n) is the ratio of the sine of the angle of incidence to the sine of the angle of refraction.

n= Sini/Sinr OR

Refractive index (n) is the rato of the velocity of light in air to the velocity of light in glass n= Velocity of light in air (Va)/Velocity of light in glass (Vg) Or Refiactive index, n is the constant number which expresses how many times or to what extent @ light ray bends when passing through different medium, Absolute reffactive index (n,) is the refractive index between Yacuum or air and any other medium.

The tefiactive indices between air and some common media is given below Medium Reviactive index (n) Diamond 2417 Ethane 1360 ass (Crown) 120 ust 1553 Water at 20°C0 133 Aira to) 1.po029

Example 2

Real and Apparent Depth

Real depthis the actual height measured without taking acount any reftaction of ight

The Concept of Critical Angle and Total Internal Reflection of Light

Critical angle Critical angles the angle of incidence (j) for which the angle of refraction (1) is equal to 90" Itis obtained when light rays moves from a dense medium to a less dense medium, For refractive index nSini/sine But i= Critical angle, ©

n=SinCl n=Sinc c= Sin I (a)

Total Internal Refraction

This oceurs when a light ray froma less dense medium is reflected into the denser medium atthe boundary separating the two media, Conditions for tral internal reflection to oceurinelude the following

• Light must be travelling from a more dense to less dense medium.

2 Light must incident atthe boundary at an angle greater than the critical angle (C), Optical fibres These are very thin tubes of plastic or glass and because they are so thin they can bend without breaking, so they can carry light around the comers

Uses oF optical fibres

• Used in telecommunications to carry telephone calls over vast distance, without Joss of

intensity and without interference. u

• Used in endoscope to view inside a patient body for example inside stomach. Light is

carried into the stomach through a bunch of fibres and is reflected into small camera, which then displays a picture ona sere. ‘The Occurance of Mirage Explata the occurrence of mirage This is the phenomenon inwhich an object appears to be at an incorrect position due to the bending of light ays from the object.

Mirages occur during hot days, oe ee i Refraction of Light by Rectangular Prism ‘The Passage of Light through a Triangular Prism Trace ihe passage of light through a ilangular prism Deviation of light ina prism isthe changing in direction of the incident ray when it entershits a trianglar glass pris, Where i isthe angle of incidence ss the angle of deviation ‘The minimum engle of deviation ( qm) In order to determine the minimum angle deviating (Qm) then we must st triangular Glass prism

a follows ed Ba —— Fk bas Se SS RS; Angular ke

The Dispersion of White Light

Demonstrate the dispersion of white light Dispersion of light isthe spliting up of light beam (white light) imo its seven components of colour by prism, Spectrum is the patch or band of colours which comprise / constitute seven component of white light Pure section is the patch or band of colours in which the colours are clearly separated In order to produce pure spectrum then we must use two converging lenses (convex lenses),

m\ Af! Ls Fe _-_. if oT ce When colours of spectrum are combined, they form whit light In order o combine colours ofthe spectrum, weneed two triangular glass prisms and one lens Impure speetrumthe band/patch of colours which overlap and are not seen clearly The rainbow:a bow-shaped spectrum of seven colours of white light formed when white light undergoes dispersion within the rain drops because water is denser than air, so has a large

refractive index. A rainbow can be demonstrated as follows: Spray some water into the ar in a direction opposite to that of the sun, Look at the water shower while you face away fom the sun. You will see the colour of the spectrum of white light in the falling drops of water. The spectrum so formed hasthe shape like @ bow. So itis called rainbow.

There are two maia types of rainbow 1 Primary rainbow 2 Secondary rainbow Primary rainbow This is formed when light undergoes one or single total intemal reflection in the water droplets In this type of the rainbow the violet colour ison the inside of the bow while the red colour is on the outside The Angles of Deviation and Minimum Deviation Determine the angles of deviation and minimum deviation Finding the refractive index (n) of elass by using the deviation of ight in a prism:

Reftaeting angle of prism is A SnelP’s law

Sin e? = nsin i From Geometry of figure lear The total angle of deviation (s) is the angle between the direction orf the incident ray and the emergent ray Again from the Geometry Q is given by Seitr-A When the deviation is a minimum (Sm) the passage of light through the prism will be symmetrical so

This means that

A+ Smin=2i=2r

Therefore;

Sin (A/2) Where

Smin ~The angle of minimum deviation

A Simple Prism Binocular

Construct a simple prism binocular Simple prism binocular

Porroprism Roof pram

Eyepiece Eyepiece

Objective Onjective

Colours of Light

The Component of White Light

Explain the component of white light There are two types of colour of light

• Primary colour of light

2 Secondary colour of light Primary colour of light These are basic (fundamental ) Colour of light to which the eye is most sensitive Primary Colour of light Include the following 1 Red 2 Green 3 Blue Secondary colours of light Colour mixing by Addition This is the process of combining primary colours of light without loss any colour to form

Colours of White Light

Recombine colours of white light When all white light (Red , Blue and Green)Combineforms WHITE LIGHT. Complementary colours of light: These are the colours which produce white light when . Red + Blue+ Green – White light . Red + Cyan – White light

• Blue + Yellow – White light
• Green + Magenta – White light

The Appearances of Coloured Object under White Light There are two types of coloured paint pigments) which Include the following . Primary coloured pigment (paints) 2 Secondary coloured pigment (pains) Primary, Secondary and Complementary Colours of Light

Primary Coloured pigments

The primary coloured pigments inelude: Yellow, Cyan and Magenta Secondary colour pigments These are coloured pigments which are formed when two primary colours eombine, whichis

Difference between Additive and Subtractive Combination of Colours

Colour Mixing by Substration

Is the process of mixing two primary coloured paints ( pigments) to form secondary colour white

Example3

• Magenta + Cyan
• Magenta = ( Blue) + (Red)
• Cyan= (Blue) + (green)

Magenta + Cyan = Blue

Example 4

• Magenta + yellow

. Magenta = (Blue) + (Red) . Yellow = (Green) + (Red) The colour which is common to both red will appear while blue and green will disappear. a Hence Magenta + Yellow = Red

Example

• Cyan + yellow
• Cyan = (Blue) + Green)

. Yellow = (Red) + (Green) The colour which is common to both green will appearwhile Blue and Red will diseppear Henee Cyan + Yellow = Green Refraction of Light by Lenses Diffference between Convex and Concave Lenses Distinguish between conver and concave lenses A ens isa transparent medium bounded by two surfaces of regular shape. There are two major categories of lenses which include ‘The Terms Focal Length, Principle Focus, Principle Axis and Optical Centre

as Applied to Lenses Explain the terms focal length, principle focus, principle axis and optical cenire as applied to lenses Optical center is « geometric center of a lens. Center of curvature is the center of the sphere in which a lens is a part. Principal axis is an imaginary line which passes through the optical center of the lens at right angle to the lens. Prineiple focus is 2 point through which all rays traveling

close and parallel to the principal axis pass through. ‘The Focal Length ofa Lens Determine practically the focal length of a tens to note that the the principal focus isnot the helfway between the optical centre and the centre of angles withthe principal exis i called the focal plane.

Example 6

An object is 2 em high and placed 24cm from a convex lens. An image formed 72 em. find the focal length of the lens

Solution

if=Wat ln venwaa+ 2

f 18am The Immage Formed by a Lens Rays diagrams are normally used toillustratesthe formation of images by lenses. 1, A rayparallel tothe principal axis passes through or appears to diverge from the prnetpal focus after refraction.

principal ais ofthe lens.

• A ray of light through the optical center of the lens continues throughundeviated(Not

How convex and concave lenses form images ens ae — Sj —

SF wee F

oneet focal 4, al eT tea manage a fa iat uh ng ee es fe ecal ginal The position, Size and Nature of the Image formed by Lens Determine the postion, size and nature ofthe mage formed by lens ‘The nature, position and sizeof the image formed by a lens depends on the position ofthe object in relation to the type of lens. For example in converging lens when the object is between the lens and principal focus the image will be formed at the same side as the object but further from

the lens. It is virtual, erect, and magnified, The image by concave lens is erect, virtual and reduced

• Takea convex lens. Find sts approximate focal ength in a way described in Activity 11

2 Draw five parallel straight lines, using chalk, on a long ‘Table such that the distance between the successive lines is equal to the focal length ofthe lens

• Place the lens on a lens stand, Place it om the central line such that the optical centre of

the lens fies just over the line

• The two lines on either side of the lens correspond to F and 2F of the lens respectively

Mark them with appropriate letters such as 2P, Fi, Fsand 2F, respectively

• Place burning candle, far beyond 2F to the left. Obtain clear sherp image on a sereen

‘on the opposite side of the lens. 6 Note down the nature, position and relative size ofthe image

• Repeat this Activity by placing object just behind 2F), between Fjand 2F at F;, between

Fyand 0. Note down and tabulate your observations The nature, postion and relative size ofthe image formed by convex lens for various positions of the object is summarized inthe table below position of the object Position of the image Relative size of the Nature of the image image Highly diminished, point 1 infinity At focus Fs sie Real and inverted yon 2Fi tween Fsand 2F: Diminished Real and inverted 128; ALD Same size Real and inverted

Infinitely large oc highly 1 Facus Fy tinny enlarged Real and inverted ferween focus Fland optical Om the same side ofthe lens a8 the eat object Enlarged ‘Viral and eret 1 Take a concave lens. Place toma lens stand 2 Place a burning eandle on one side of the lens

• Look through the lens from the other side and observe the image. Try to get the image on

a screen, if possible. If not, observe the image direetly through the lens

• Note down the nature, relative size and approximate position ofthe image
• Move the candle away from the lens. Note the change in the size of the image. What

happens to the size of the image when the candle is placed too far away from the lens. 4s the object sition ofthe abject Position ofthe image Relative size of the Nature of the image image Highly diminished, point infinity At focus Fy sized Viol and erect fhe ens cenire 0 Diminished Viral and erct ‘The Magnification of the Lens Camera As we have a formula for spherical mirrors, we also have formula for spherical lenses. This

proper care of the signs of different quantities, while putting numerical values for solving The magnification produced by a lens, similar to that for spherical mirrors, is defined as the ratio of the height ofthe image and the height of the object. It is represented by the leter m. If his the height of the object and his the height of the image given by a lens, then the magnification

Example 7

A concave lens has focal length of 15 om. At what distance should the objet from the lens be placed so that it forms an image at 10 cm from the lens? Also, find the magnification produced by the lens.

Solution

Since, Ly /w=1/F

oe Mus tiy=t/E

the object. The Relationship between Focal Length (f) Object Distance (u) and Image Distance (v) as Applied to Lenses Kempe An object is placed 12 em from converging las of Focal length 18 cm. Find the postion ofthe image

Solution

The image is virtual,