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 virtual image formed in the rarer medium of refractive index n₁. 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

(i)

For destructive interference

=> V = 100 cm a real image on the other side, 100 cm away from the surface.