Question

A tiny air bubble, trapped inside a glass cube of side a, appears to be at distances x₁ and x₂ , respectively, when viewed from two opposite faces of the cube. The refractive index, of glass, and the actual distance (x) of the air bubble, from the first of the two faces, are then equal, respectively, to

(1) \((\frac{x_1+x_2}{a})\) and \((\frac{x_1+x_1}{a})\)

(2) \((\frac{x_1+x_2}{a})\) and \((\frac{ax_2}{x_1+x_2})\)

(3) \((\frac{a}{x_1+x_2})\) and \((\frac{ax_2}{x_1+x_2})\)

(4) \((\frac{a}{x_1+x_2})\) and \((\frac{ax_1}{x_1+x_2})\)

Answer 1

(4) \((\frac{a}{x_1+x_2})\) and \((\frac{ax_1}{x_1+x_2})\)

The apparent distance, of the air bubble from the first face, is 1/μ times its real distance (= x) from that face.

Hence x₁ = x/μ

For the opposite face, the real distance, of the air bubble, would be (a–x). 

Hence x₂ = (a-x/μ)

Dividing, we get