Question

A transparent sphere of radius 6cm is kept in air. An object is placed at 12 cm distance from

the surface of the sphere and its real image is formed at the same distance from the second

surface of the sphere. Find the refractive index of the material of the sphere ?​

Answer 1

Given info : A transparent sphere of radius 6cm is kept in air. An object is placed at 12 cm distance from the surface of the sphere and its real image is formed at the same distance from the second surface of the sphere.

To find : The refractive index of the material of the sphere.

solution : see diagram, here it is clear that a ray passing through sphere is parallel to principal axis.

for 1st surface,

using formula, μ₂/v - μ₁/u = (μ₂ - μ₁)/R

here, refractive index of the sphere = μ₂

refractive index of air, μ₁ = 1

image distance, v = ∞

object distance, u = x = -12cm

radius of curvature, R = 6cm

so, μ₂/∞ - 1/-12 = (μ₂ - 1)/6

⇒1/12 = (μ₂ - 1)/6

⇒1/2 + 1 = μ₂

⇒μ₂ = 3/2 = 1.5

Therefore the refractive index of the sphere is 1.5