Question

A coin is resting on the bottom of an empty container. The container is then fi lled to the brim three times, each time with a diff erent liquid. An observer (in air) is directly above the coin and looks down at it. With liquid A in the container, the apparent depth of the coin is 7 cm, with liquid B it is 6 cm, and with liquid C it is 5 cm. Rank the indices of refraction of the liquids in descending order (largest fist).
a. nC, nA, nB
b. nA, nB, nC
c. nB, nA, nC
d. nC, nB, nA
e. nA, nC, nB

Answer 1

when we placed in the container of real depth assuming = d

if the container filled with liquid A then its apparent depth d' = 7cm

so the refractive index nA = real depth / apparent depth

                                       = d/7cm = 0.1428d

if the container filled with liquid B then its apparent depth d' = 6cm

so the refractive index nB = real depth / apparent depth

                                       = d/6cm = 0.166d

if the container filled with liquid C then its apparent depth d' = 5cm

so the refractive index nC = real depth / apparent depth

                                       = d/5cm = 0.2d

Since the refractive index is inversely proportional to the apparent depth

then the refractive indices are nC > nB > nA