OPTOMETRY · SEMESTER 2 Thin lenses 1 Physical and Geometric Optics START READING NOTES Contents of This Topic Thin lenses 1 TERMINOLOGY OF THIN LENSES FOCAL LENGTHS F2Thin Lenses I F1Thin Lenses I IMAGE FORMATION BY GRAPHICAL CONSTRUCTION DIVERGING LENS LINEAR MAGNIFICATION Object Size (O) CONJUGATE POINTS Thin lenses 1 THIN LENSES I CHAPTER CONTENTS TERMINOLOGY OF THIN LENSES………………………………………………………………………………………………………………… 1 FOCAL LENGTHS ………………………………………………………………………………………………………………………………………… 0 REAL AND VIRTUAL …………………………………………………………………………………………………………………………………….. 2 IMAGE FORMATION BY GRAPHICAL CONSTRUCTION …………………………………………………………………………………. 2 LINEAR MAGNIFICATION……………………………………………………………………………………………………………………………… 5 CONJUGATE POINTS…………………………………………………………………………………………………………………………………… 5 TERMINOLOGY OF THIN LENSES A thin lens is one whose thickness is very small in comparison to its focal length1 . A typical thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a portion of either a sphere or a plane. A lens is used to direct or control rays of light. The refraction of light at the surface of a lens depends on its shape, its index of refraction, and the nature of the medium surrounding it (usually air), in accordance with Snell’s Law. Lenses are commonly used to form images by refraction in spectacles and in optical instruments such as cameras, telescopes and microscopes. 1 Although any contact lens must be considered a thick lensThin Lenses I Lenses can be placed in two groups. Those in the one group are thicker at the centre than at the rim. They are known as converging lenses (or convex lenses). They refract incident parallel rays so that they converge at a point on the opposite side of the lens. The others are thinner at the centre than at the rim. They are known as diverging or concave lenses. They refract incident parallel rays so that they appear to diverge from a point located on the incident side of the lens. Any object viewed through such a lens always appears erect and smaller than when viewed with the unaided eye. A meniscus (meaning crescent-shaped) lens has one convex surface and one concave surface. The principal axis or optical axis of a lens is the line joining the centres of curvature of the two surfaces. Rays making small angles with the optical axis are referred to as paraxial rays. The optical centre of a thin lens is such that any ray passing through that point is not deviated. For the cases we will deal with in this course, the optical centre of a lens can conveniently be thought of as the geometric centre of the lens. Figure 4.1: Different types and shapes of lenses FOCAL LENGTHS There are two points on the optical axis which need special attention. The following figure shows a pencil of paraxial rays from an object at an infinite distance from a converging lens. As such, the pencil will be effectively parallel on reaching the lens. These rays are refracted through the point F2 which is called the second principal focus or second focal point of the lens. The distance from the optical centre to F2 is called the second focal length of the lens and will be referred to by the symbol f2. Figure 4.2: Illustration of the second focal point of a converging lens Similarly, in the next figure, there is the point F1 from which paraxial rays, after refraction by the lens, emerge parallel to the axis. F1 is referred to as the first principal focus or first focal point of the lens, and the distance from the optical centre to F1 is referred to as the first focal length of the lens and is given the symbol f1. F2Thin Lenses I Figure 4.3: Illustration of the first focal point of a converging lens If the lens is thin, and the medium on each side of the lens is the same, then the numerical values of f1 and f2 will be identical. Note that the diagrams show lenses with exaggerated thicknesses and rays that make greater angles with the optical axis than should be the case for paraxial rays. This has been done simply to allow the clear exposition of the refraction at each surface. When “the focal length” of the lens is stated without specifying it to be the first or second focal length, it must always be inferred that this means the second focal length of the lens. In the case of a diverging lens, there are two similar principal foci. The next figure shows the point F1, the first principal focus or first focal point of a diverging lens. Rays directed towards this point emerge from the lens parallel to the optical axis. Once again, the distance from the optical centre to F1 is the first focal length, f1. F1 can be seen to be on the opposite side of the lens compared to the incident light. Figure 4.4: Illustration of the first focal point of a diverging lens Similarly, the second principal focus or second focal point (designated F2) is formed where rays that are incident on a diverging lens parallel to the optical axis appear to diverge from. The distance from the optical centre to F2 is thus the second focal length of the lens. The figure shows that the second focal point lies on the same side as the incident light. As before, if the lens is thin and the media on each side of the lens are identical in refractive index, then the focal lengths have the same magnitude. F1 F1Thin Lenses I Figure 4.5: Illustration of the second focal point of a diverging lens REAL AND VIRTUAL The major usefulness of lenses is their ability to form images of an object. The object may be self-luminous, giving off its own light (like the sun or a light bulb), or it may reflect the light that falls on it (like an apple or a page of this book). In either case, an image of the object is formed where light rays that come from points on the object intersect or at the points from which