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

Explanation

Radius of curvature of curved surface R =20 cm
Refractive index of medium `n_2 =1.5, `
Refractive index of air `n_1 = 1.0`
Object distance U = - 100 cm
Equation of refraction by curved surface
`(n_2)/(v) - (n_1)/(u) = (n_2 -n_1)/(R)`
`(1.5)/(v) - (1)/(-100) = (1.5 - 1.0)/(20)`
`therefore (1.5)/(v) = -(1)/(100) + (0.5)/(20)`
`therefore (1.5)/(v) = (1.5)/(100)`
`therefore v= (1.5 xx 100)/(1.5)`
`therefore v = 100 cm`
Thus, image will be obtained at 100 cm distance from surface in direction of incident ray.