Question

Light is incident normal to liquid layer of refractive index 1.33 that lies on top of a flat
flint glass. The light will take 3.73x10-11s of more time to traverse through these two
layers than the same distance in air. Find the refractive index of flint glass if the widths of
liquid and glass layers are 1.5 cm and 1.0 cm.
(a) 1.42
(b) 1.64
(c) 1.45
(d) 1.62​

Answer 1

Light is incident normal to liquid layer of refractive index 1.33 that lies on the top of a flat flint glass. The light will take 3.73 × 10¯¹¹ s of more time to transverse through these two layer than the same distance in air.

To find : The refractive index of flint glass if the widths of liquid and glass layers are 1.5cm and 1.0 cm respectively.

solution : time taken by light to penetrate liquid and glass layers - time taken by light to penetrate the very width in air = t

⇒(μ₁x₁)/C + (μ₂x₂)/C - (x₁/C) - (x₂/C) = t

⇒(μ₁ - 1)x₁ + (μ₂ - 1)x₂ = Ct

now putting, x₁ = 1.5 cm, x₂ = 1.0 cm, μ₁ = 1.33, C = 3 × 10^8 m/s and t = 3.73 × 10¯¹¹ s

⇒(1.33 - 1) × 1.5 × 10¯² + (μ₂ - 1) = 3 × 10^8 × 3.73 × 10¯¹¹

⇒0.495 + (μ₂ - 1) = 1.119

⇒μ₂ = 1.624 ≈ 1.62

Therefore the refractive index of flint glass is 1.62