Question

(i) Derive the mathematical relation between refractive indices n1 and n2 of two radii and radius of curvature R for refraction at a convex spherical surface. Consider the object to be a point since lying on the principle axis in rarer medium of refractive index n1 and a real image formed in the denser medium of refractive index n2. Hence, derive lens maker's formula.
(ii) Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20 cm. The distance of light source from the glass surface is 100 cm. At what position is the image formed?

Answer 1

Thus the position of the images is at v = 100 cm

Explanation:

Light from a point source in air falls on a convex spherical glass surface of refractive index 1.5 and radius of curvature 20 cm. The distance of light source from the glass surface is 100 cm. At what position is the image formed?

Solution:

Refractive index, μ = 1.5

Radius of curvature, R = 20 cm

Object distance, u = 100 cm

Image distance, v = ?

We know

μ2 / v   −   μ  1 / u  = μ  2 −μ  1  /   R

​μ2 = 1.5

μ  1  = 1

1.5 / v = 0.5 / 20 - 1 / 100

1.5 / v = 3 / 200

v = 200 / 3 x 1.5

v = 100 cm

Thus the position of the images is at v = 100 cm