Question

Three layers of three different transparent media (of refractive indices n₁ , n₂ and n₃ , respectively) have thicknesses d₁ , d₂ and d₃ , respectively. Their total apparent depth, when viewed from above, would appear to be (nearly)

(1) \(\frac{d_1}{n_2}+\frac{d_2}{n_3}+\frac{d_3}{n_1}\)

(2) \(\frac{d_1}{n_2}-\frac{d_2}{n_3}-\frac{d_3}{n_1}\)

(3) \(\frac{1}{n_1n_2n_3}\) (d₁n₂n₃+d₂n₃n₁+d₃n₁n₂)

(4) \(\frac{1}{n_1n_2n_3}\)  (d₁n₁n₂+d₂n₂n₃+d₃n₃n₁)

Answer 1

(3) \(\frac{1}{n_1n_2n_3}\) (d₁n₂n₃+d₂n₃n₁+d₃n₁n₂)

The apparent depth, of a layer of a medium of refractive index μ, is (1/μ) times its real depth. Hence the total apparent depth, of the three layers, would be