Question
A homogenous column of water $\left( \ _{a}\mu_{w} = \frac{4}{3} \right)$ of height 8.0 cm fills the space above a 9.0 cm thick glass $\left( \ _{a}\mu_{g} = \frac{3}{2} \right)$ slab. Observers A and B are in air just outside the top and the bottom whereas the observers C and D are inside just below the top and above the bottom. The total thickness of glass plus water observed by these observers are
Options
Solution
Sol. Key concept: For paraxial viewing through plane layers, apparent thickness scales with refractive index.
For an observer in refractive index n₀, a layer of thickness t and refractive index n contributes apparent thickness n₀t/n. Here the water thickness is 8 cm with n_w = 4/3, and the glass thickness is 9 cm with n_g = 3/2.
$$T_{A} = T_{B} = \frac{8}{4/3} + \frac{9}{3/2} = 6 + 6 = 12\ cm$$
Observer C is just inside water, so its own water layer is unaltered while the glass thickness is rescaled.
$$T_{C} = 8 + 9\frac{4/3}{3/2} = 8 + 8 = 16\ cm$$
Observer D is just inside glass, so the glass thickness is unaltered while the water thickness is rescaled.
$$T_{D} = 9 + 8\frac{3/2}{4/3} = 9 + 9 = 18\ cm$$
All four statements are correct. Parentheses are essential when applying the successive refractive-index factors.
Create a free account to view solution
View Solution Free