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Downloaded from https:// www.studiestoday.com, , , , Refraction Through A Lens, , , , SYLLABUS, , Lenses (converging and diverging) including characteristics of the images formed (using ray diagrams only),, magnifying glass, location of images using ray diagrams and thereby determining magnification., , , , Scope of syllabus : Types of lenses (converging and diverging), convex and concave action of a Jens as a set of, , piism, technical terms : centre of curvature, radius of curvature, principal axis, foci, focal plane and focal length,, , detailed study of refraction of light in spherical lenses through ray diagrams, formation of images — principal, , rays or construction rays, location of images from ray diagrams for various positions of a small linear object on, , the principal axis, characteristics of images, sign convention and direct numerical problems using the lens formula _, are included (derivation of formula not required). Scale drawing or graphical representation of ray diagrams, , not required., , Power of a lens (concave and convex), simple direct numicrical problems. Magnifiying glass or simple microscope,, , location of image and magnification from ray diagram only (formula and numerical problems nor included)., , Applications of lenses., , , , , , , , , , (A) LENS AND REFRACTION OF LIGHT THROUGH A LENS, , , , 5.1 LENS A convex lens may be of the following three, , We are all familiar with the use of lenses in kinds :, spectacles. We define a lens as follows : (i) bi-convex or double-convex or equi-convex,, , , , eae ai (ii) plano-convex, and, (iii) concavo-convex., , Fig. 5.1 shows the shape of different kind of, convex lenses., , , , A plane surface can be treated as a spherical, surface of infinite radius of curvature., , Kind of lenses : Lenses are of two kind :, , (1) converging or convex lens, and BLCONVEX PLANO-CONVEX | CONCAVO, (2) diverging or concave lens. CONVEX, , Fig. 5.1 Convex lenses, , ge a A biconvex lens has both its surfaces convex,, , _ A convex lens is thick in its middle and 4 plano-convex lens has one surface plane and the, thin at the periphery. In other words, a lens which other surface convex, while a concavo-convex, bulges out in the middle, is the convex lens. A Jens has one surface convex and the other surface, , light beam converges on passing through such a concave such that it is thicker in the middle as, lens, so it is also called the converging lens. compared to its periphery., , Downloaded from https:/?*www.studiestoday.com

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Downloaded from https:// www.studiestoday.com, , (2) Diverging or concave lens, A concave lens is thick at its periphery, and thin in the middle. In other words, a lens, which is bent inwards in the middle, is the, concave lens. Such a lens diverges the light rays, incident on it, so it is also called the diverging, lens., A concave lens may be of the following three, kinds :, (i) bi-concave or double-concave or equi-concave,, (ii) plano-concave, and, (iii) convexo-concave., Fig. 5.2 shows the shape of different kind of, concave lenses., , PLANO-CONCAVE CONVEXO, CONCAVE, , BI-CONCAVE, Fig. 5.2 Concave lenses, , A bi-concave lens has both its surfaces, concave, a plano-concave lens has one of its, surface plane and the other surface concave, while, a convexo-concave lens has one surface concave, and the other surface convex such that it is, thinner in the middle as compared to its periphery., , , , Note : Both the concavo-convex and the, convexo-concave lenses have one surface, convex and the other surface concave, but they, differ in their shape and action. A concavoconvex lens is thicker in the middle and has a, converging action on a light beam, while a, convexo-concave lens is thinner in the middle, and has a diverging action on a light beam., , , , , , , , 5.2 ACTION OF A LENS AS A SET OF, PRISMS, , We have read the refraction of light through, a prism. The refraction of light through a lens can, be understood in a simple way by considering a, lens as being made up of a set of prisms as, , |, Ca, J, V, , (a) Convex lens, Fig. 5.3 A lens being made up of a set of prisms, , J, U, U], A, TEX, (b) Concave lens, , To make it further simple, the prisms in the, central portion of the lens, shown in Fig. 5.3, may, be treated as a rectangular slab. Then the lens can, be considered as being made up of a rectangular, slab at the centre and one prism on either side, of it as shown in Fig. 5.4., , , , , , , , , , (a) Convex lens (b) Concave lens, , Fig. 5.4 A lens being made up of a rectangular slab at the, centre and one prism on either side of it, , A convex lens in its upper part has a prism, with its base downwards and in its lower part, has a prism with its base upwards as shown in, Fig. 5.4(a). On the other hand, a concave lens in, its upper part has a prism with its base upwards, and in its lower part has a prism with its base, downwards as shown in Fig. 5.4(b)., , Convergent action of a convex lens, , Let us consider the refraction of parallel rays, of light A, B and C incident on the prisms in the, upper, central and the lower parts of convex lens., We know that a ray of light incident on a prism,, on refraction through it, always bends towards the, base of prism. Therefore the prism in the upper, part of convex lens bends the incident ray A, downwards, while the prism in the lower part of, convex lens bends the incident ray C upwards, (Fig. 5.5). The central part which is a parallel, sided glass slab passes the ray B normally, incident on it, undeviated. Thus the set of, prisms forming a convex lens converges the, , Pan, , , , www.

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Downloaded from https:// www.studiestoday. com, , parallel rays to a point F. Therefore a convex lens, has a converging action on the incident light, rays., , , , , , , , , , , , Cc, , Fig. 5.5 Convergent action of a convex lens, , Divergent action of a concave lens, , In Fig. 5.6, the prism in the upper part of the, concave lens bends the incident ray A upwards, ie., towards its base, while the prism in the lower, part of the concave lens bends the incident ray, C downwards i.e., towards its base. The central, part, which is a parallel sided glass slab, passes, the normally incident ray B undeviated. Thus, the, set of prisms forming a concave lens diverges the, parallel rays as if they are coming from a, common point F situated on the side of rays, incident on the lens. Therefore, a concave lens, has a diverging action on the incident light rays., , , , Fig. 5.6 Divergent action of a concave lens, , 5.3 TECHNICAL TERMS RELATED TO A, LENS, , (1) Centre of curvature : A lens has two, surfaces. Each surface of the lens is a part, of a sphere. The centre of the sphere whose, part is the. lens surface, is called the centre, of curvature of that surface of the lens. Since, a lens has two spherical surfaces, so there, are two centres of curvature of a lens., In Fig. 5.7, C, and C, are respectively, the centres of curvature of the two surfaces, 1 and 2 of the lens., , , , &, , , , Fig. 5.7 Centre of curvature, principal, axis and optical centre, , , , Note : For a convex lens, Cc, is to the right, of surface 1 and Cc, is to the left of surface 2,, while for a concave lens, C, is to the left of, surface 1 and C, is to the right of surface 2., , , , , , , , (2) Radius of curvature : The radius of the, sphere whose part is the lens surface, is, called the radius of curvature of that surface, of the lens. In Fig. 5.7(a), PC, and PC, are, the radii of curvature of the two surfaces 1, and 2 of the convex lens. If the lens is thin,, then PC, = OC, and PC, = OC,. Similarly, in Fig. 5.7(b), P,C, and P,C, are the radii of, curvature of the two surfaces 1 and 2 of, the concave lens. If the lens is thin, then, P,C, = OC, and P,C, = OC,. The point O is, called the optical centre. Thus for a thin lens,, the radius of curvature of a surface of lens, is equal to the distance of centre of curvature, of that surface from the optical centre. For, an equi-convex or equi-concave lens, the, radii of curvature of both the surfaces are, equal (i.e, OC, = OC,). The lenses shown, in Fig. 5.7 (a) and (b) are not equi-convex, and equi-concave since the radii of curvature, of the two surfaces OC, and OC, are not, equal., , Principal axis : Jt is the line joining the, centres of curvature of the two surfaces of, the lens. In Fig. 5.7, the line C,C, is the, principal axis. It can extend on either side of, the lens., , (3), , “Downloaded from https:}www.studiestoday.com

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Downloaded from https:// www.studiestoday.com, (4) Optical centre : It is a point on the principal (5) Principal foci : A light ray can enter a lens, , axis of the lens such that a ray of light from either side, therefore, a lens has two, , passing through this point emerges parallel principal foci. If medium is same on either, , to its direction of incidence. It is marked by side of the lens, the two foci are situated at, , the letter O in Fig. 5.7. The optical centre is equal distances from the optical centre,, , thus the centre of lens. one on either side of the lens. These are, , Since the central portion of a thick lens can known as the first focal point (or first focus), , be considered to be a parallel sided glass slab, F, and the second focal point (or second, therefore a ray of light incident at the central focus) F,., , portion of the lens, while passing through the, optical centre O, is slightly displaced parallel to, its original direction. In Fig. 5.8, the emergent ray, is thus parallel to the incident ray., , First focal point, , , , , , (a) Convex lens (b) Concave lens, Fig. 5.8 Optical centre (thick lens), , Note : In Fig 5.8, the lateral shift of the, ray has been shown quite large, but actually it, is very small., , , , , , , , , , , , Generally the lens is thin, so the lateral shift (a) Convex lens, is small enough and it can be ignored. Therefore,, a ray of light directed towards the optical centre, of a thin lens can be considered to pass, undeviated and undisplaced as shown in Fig. 5.9., , oe 3 :, ke-— f, —91, (6) Concave lens, , Fig. 5.10 First focus and focal length, , , , , , (a) Convex lens (b) Concave lens, Fig. 5.9 Optical centre (thin lens), , , , , Thus,

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PRINCIPAL AXIS, , $— 1,, (a) Convex lens, , PRINCIPAL AXIS, , , , e— 1,1, (b) Concave lens, Fig. 5.11 Second focus and focal length, , , , (6) Focal plane : A plane normal to the principal, axis, passing through the focus, is called the, focal plane. A lens has two focal planes., , (i) First focal plane : A plane passing, through the first focal point and normal, to the principal axis of the lens, is, called the first focal plane., , (ii) Second focal plane : A plane passing, through the second focal point and, normal to the principal axis of the lens,, , is Called the second pia ee as, , , , Downloaded from https:// www. studiestoday. com, Second focal point (7) F, , ‘ocal length : The distance of focus (or focal, point) from the optical centre of lens, is, called its focal length. A lens has two focal, lengths., , (i) First focal length : The distance from, the optical centre O of the lens to its, first focal point F, is called the first, focal length f, of the lens. In Fig. 5.10,, it is shown as OF, = f,., , (ii) Second focal length : The distance, from the optical centre O of the lens to, the second focal point F, is called the, second focal length f, of the lens. In, Fig. 5.11, it is shown as OF, = f,., , , , , , lote : (1) If the medium on both sides of a, lens is same, its first and second focal lengths are, equal, i.e., f,; = f, (numerically)., , (2) Usually, when we say focus, we mean the, second focal point. Hence the focal length of a, lens implies the second focal length of the lens., , (3) A convex lens has a real focus (because, the parallel rays incident on a convex lens, actually pass through this point), while in a, concave lens the focus is virtual (because the, parallel rays incident on a concave lens do not, actually pass through this point, but they appear, to diverge from this point)., , (4) Only a beam of light incident parallel to, the principal axis converges to a single point F,, (the focus) on the principal axis after refraction, through the convex lens. If the parallel beam of, light is incident obliquely (i.e., the rays are not, parallel to the principal axis of the lens), it does, not converge at the principal focus F,, but it, , , , , , Fig. 5.12 Refraction of an oblique parallel, , or pele a convex lens