ICSE Class 10 Physics Chapter 05 Refraction Through A Lens

Chapter 5: 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 lens as a set of prism, 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 numerical problems. Magnifying glass or simple microscope, location of image and magnification from ray diagram only (formula and numerical problems not included). Applications of lenses.

Section A: Lens And Refraction Of Light Through A Lens

5.1 Lens

We are all familiar with the use of lenses in spectacles. We define a lens as follows:

A lens is a transparent refracting medium bounded by either the two spherical surfaces or one surface spherical and other surface plane.

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

(2) diverging or concave lens.

Converging or convex lens

A convex lens is thick in its middle and thin at the periphery. In other words, a lens which bulges out in the middle, is the convex lens. A light beam converges on passing through such a lens, so it is also called the converging lens.

A convex lens may be of the following three kinds:

(i) bi-convex or double-convex or equi-convex,

(ii) plano-convex, and

(iii) concavo-convex.

Fig. 5.1 shows the shape of different kind of convex lenses.

[Image shows three lens shapes labeled: BI-CONVEX, PLANO-CONVEX, CONCAVO-CONVEX]

Fig. 5.1 Convex lenses

A biconvex lens has both its surfaces convex, a plano-convex lens has one surface plane and the other surface convex, while a concavo-convex lens has one surface convex and the other surface concave such that it is thicker in the middle as compared to its periphery.

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.

[Image shows three lens shapes labeled: BI-CONCAVE, PLANO-CONCAVE, CONVEXO-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 concavo-convex 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 shown in Fig. 5.3.

[Image shows a convex and concave lens made up of prisms]

Fig. 5.3 A lens being made up of a set of prisms

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.

[Image shows convex and concave lenses with rectangular slabs and prisms]

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 parallel rays to a point F. Therefore a convex lens has a converging action on the incident light rays.

[Image shows three parallel rays converging through a convex lens to point F]

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 i.e., 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.

[Image shows three parallel rays diverging through a concave lens as if from point F]

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, C1 and C2 are respectively the centres of curvature of the two surfaces 1 and 2 of the lens.

(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), FC1 and PC2 are the radii of curvature of the two surfaces 1 and 2 of the convex lens. If the lens is thin, then PC1 = OC1 and PC2 = OC2. Similarly in Fig. 5.7(b), P1C1 and P2C2 are the radii of curvature of the two surfaces 1 and 2 of the concave lens. If the lens is thin, then P1C1 = OC1 and P2C2 = OC2. 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 OC1 and OC2 are not equal.

(3) Principal axis

It is the line joining the centres of curvature of the two surfaces of the lens. In Fig. 5.7, the line C1C2 is the principal axis. It can extend on either side of the lens.

[Image shows convex and concave lenses with labeled centers of curvature and principal axes]

Fig. 5.7 Centre of curvature, principal axis and optical centre

Note: For a convex lens, C1 is to the right of surface 1 and C2 is to the left of surface 2, while for a concave lens, C1 is to the left of surface 1 and C2 is to the right of surface 2.

(4) Optical centre

It is a point on the principal axis of the lens such that a ray of light passing through this point emerges parallel to its direction of incidence. It is marked by the letter O in Fig. 5.7. The optical centre is thus the centre of lens.

Since the central portion of a thick lens can be considered to be a parallel sided glass slab, therefore a ray of light incident at the central 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.

[Image shows lateral shift of ray through optical centre of convex and concave lenses]

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 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.

[Image shows ray through optical centre of convex and concave lenses without deviation]

Fig. 5.9 Optical centre (thin lens)

Thus,

Optical centre of a thin lens is the point on the principal axis of lens such that a ray of light directed towards it, passes undeviated through it.

(5) Principal foci

A light ray can enter a lens from either side, therefore, a lens has two principal foci. If medium is same on either side of the lens, the two foci are situated at equal distances from the optical centre, one on either side of the lens. These are known as the first focal point (or first focus) F1 and the second focal point (or second focus) F2.

First focal point

For a convex lens, the first focal point is a point F1 on the principal axis of the lens such that the rays of light coming from it, after refraction through the lens, become parallel to the principal axis of the lens [Fig. 5.10 (a)].

[Image shows first focal point of convex lens with converging rays becoming parallel]

Fig. 5.10 First focus and focal length (a) Convex lens (b) Concave lens

For a concave lens, first focal point is a point F1 on the principal axis of the lens such that the incident rays of light appearing to meet at it, after refraction from the lens become parallel to the principal axis of the lens [Fig. 5.10 (b)].

Second focal point

For a convex lens, the second focal point is a point F2 on the principal axis of the lens such that the rays of light incident parallel to the principal axis, after refraction from the lens, pass through it [Fig. 5.11 (a)].

[Image shows second focal point of convex and concave lenses]

Fig. 5.11 Second focus and focal length

For a concave lens, second focal point is a point F2 on the principal axis of the lens such that the rays of light incident parallel to the principal axis, after refraction from the lens, appear to be diverging from this point [Fig. 5.11 (b)].

(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 focal plane.

(7) Focal 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 F1 is called the first focal length f1 of the lens. In Fig. 5.10, it is shown as OF1 = f1.

(ii) Second focal length

The distance from the optical centre O of the lens to the second focal point F2 is called the second focal length f2 of the lens. In Fig. 5.11, it is shown as OF2 = f2.

Note: (1) If the medium on both sides of a lens is same, its first and second focal lengths are equal, i.e., f1 = f2 (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 F2 (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 lenses), it does not converge at the principal focus F2, but it converges at some point B in the second focal plane of the lens as shown in Fig. 5.12. The point B lies on the second focal plane where the ray AO, through the optical centre O of the lens, meets the focal plane.

[Image shows refraction of oblique parallel beam through convex lens]

Fig. 5.12 Refraction of an oblique parallel beam by a convex lens

Similarly, if a parallel beam of light is incident obliquely on a concave lens, after refraction it appears to diverge from a point B in the second focal plane as shown in Fig. 5.13.

[Image shows refraction of oblique parallel beam through concave lens]

Fig. 5.13 Refraction of an oblique parallel beam by a concave lens

(5) The focal length of a lens depends on the following two factors:

(i) The refractive index of the material of lens relative to its surrounding medium. If a lens is placed in water instead of air, its focal length increases.

(ii) The radii of curvature of the two surfaces of lens. A thick lens has less focal length than a thin lens of same material.

(6) If a part of the lens is covered, its focal length remains unchanged, only the amount of light entering the lens decreases due to which the intensity of image decreases but the position, size and nature of image formed by it do not change.

Difference between a convex and a concave lens

5.4 Refraction Of Light Through The Equi-Convex And Equi-Concave Lenses

Fig. 5.14 shows the refraction of a ray of light at the two surfaces of an equi-convex lens and an equi-concave lens. When a ray of light AB is incident on a lens, its path changes because it suffers refraction at two surfaces of the lens marked as I and II in the diagram. First the light ray AB suffers refraction at the first surface I from air to glass, it bends towards the normal N1B at the point B. The refracted ray BC then falls on the second surface II of the lens where it now suffers refraction from glass to air, so it bends away from the normal N2C at the point C and emerges out as CD. Thus the ray of light bends at both the surfaces of lens in the same direction and hence the total deviation produced by the lens is the sum of the deviations at the two surfaces of lens.

[Image shows refraction through convex and concave lenses with labeled surfaces and normals]

Fig. 5.14 Refraction through a lens

It is clear from Fig. 5.14, that a convex lens bends the ray of light towards its middle i.e., it converges the light, while a concave lens bends a ray of light towards its edges (or away from its middle) i.e., it diverges the light.

Note: For ray diagrams, we shall consider the lens to be thin and for simplicity we shall not show the bending of ray of light at each of the two surfaces of lens separately, but we shall show the net bending towards the central part in a convex lens or away from the central part in a concave lens, at the straight vertical line passing through the optical centre.

Teacher's Note

Understanding how lenses bend light is fundamental to how your camera, magnifying glass, and eyeglasses work - all rely on these basic principles of light refraction through curved surfaces.

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