Derive the relation n 2 v − n 1 u = n 2 − n 1 R for a spherical surface and mention the assumptions adopted.

Figure shows the formation of image I of an object O on the principal axis of a convex surface with the centre of curvature C . As the aperture is small the length of NM will be taken to be nearly equal to the length of the perpendicular from the point N on the principal axis. For small angles (assuming paraxial rays) we have, tan ∠ NOM = NM OM . tan ∠ NCM = NM MC tan ∠ NIM = MN MI From the figure, we have i = ∠ NOM + ∠ NCM = NM OM + MN MC and r = ∠ NCM + ∠ NIM = NM CM - MN MI Since angles are small their sine will be equal to the angles. Applying Snell's law n 1 i = n 2 r So we have n 1 OM + n 1 MC = n 2 MC + n 2 MI or n 1 OM + n 2 M I = n 2 MC + n 1 M C Using the sign convention OM = - u , MI = + v and MC = R We have n 1 - u + n 1 v = n 2 - n 1 R This is the required relation, The assumption made in this derivation are: (1) The aperture of the surface is small. (2) the sign convention is followed. (3) The refractive index of the first medium is is less than that of the second

When two thin lenses are kept in contact, obtain the relation 1 f = 1 f 1 − 1 f 2 and discuss the nature of combined lens when f 1 > f 2 , f 1 < f 2 and f 1 = f 2 .

Consider two lenses A and B of focal length f 1 and f 2 placed in contact with each other. Let the object be placed at a point O beyond the focus of the first lens A. The first lens produces an image at I 1 Since image I 1 is real, it serves as a virtual object for the second lens B, producing the final image at I. Since the lenses are thin, we assume the optical centres of the lenses to be coincident. Let this central point be denoted by P. For the image formed by the first lens A, we get, 1 v 1 - 1 u = 1 f 1 For the image formed by the second lens B , we get 1 v - 1 v 1 = 1 f 2 Adding these equations 1 v - 1 u = 1 f 1 + 1 f 2 If the two lens system is regarded as a single one of focal length f , then we get, 1 v - 1 u = 1 f Comparing we get, 1 f = 1 f 1 + 1 f 2 When one o the lens is convex f 1 and other is concave f 2 ,than the relation becomes 1 f = 1 f 1 - 1 f 2 0 r P = P 1 + P 2 where P = powers of lenses Case 1 if convex lens has more power than concave lens P 1 > P 2 . The combines power will be positive, The combination will behave as a convex lens Case 2 When concave has more power P 1 < P 2 , P will be negative.The combination will behave as concave lens. Case 3 Both lenses are of the same power i.e P 1 = P 2 , i . e P = 0 i.e focal length is infinity. The combination will behave as a plane glass plate.

E M B I B E

ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 7

EASY

12th ICSE

IMPORTANT

Earn 100

What is meant by the power of a lens? Define dioptre and give relation between the power and the focal length of a lens.

Important Questions on Refraction of Light at Spherical Surfaces : Lenses

HARD

12th ICSE

IMPORTANT

ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 1

Derive the relation

\frac{n_{2}}{v} - \frac{n_{1}}{u} = \frac{n_{2} - n_{1}}{R}

for a spherical surface and mention the assumptions adopted.

HARD

12th ICSE

IMPORTANT

ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 2

Derive lens makers formula

$\frac{1}{f} = (n - 1) (\frac{1}{R_{1}} - \frac{1}{R_{2}})$

(symbols have their usual meanings) and discuss the dependence of focal-length on various factors.

HARD

12th ICSE

IMPORTANT

ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 3

Explain, how focal-length of a lens changes with surrounding medium. Focal-length of a lens is $f$ in air. Find its focal-length in water if $_{a} n_{g} = \frac{3}{2}$ and $_{a} n_{w} = \frac{4}{3}$ .

MEDIUM

12th ICSE

IMPORTANT

ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 4

Draw ray diagram for the formation of a point object placed at focus of a convex and concave lens. Write nature of images also.

MEDIUM

12th ICSE

IMPORTANT

ISC Physics Class 12, Part-2>Chapter 3 - Refraction of Light at Spherical Surfaces : Lenses>QUESTIONS>Q 5

When two thin lenses are kept in contact, obtain the relation $\frac{1}{f} = \frac{1}{f_{1}} - \frac{1}{f_{2}}$ and discuss the nature of combined lens when $f_{1} > f_{2}$ , $f_{1} < f_{2}$ and $f_{1} = f_{2}$ .