A tank whose bottom is a mirror is filled with water to a depth of 19.1 cm . A s

Question

A tank whose bottom is a mirror is filled with water to a depth of 19.1 cm . A small fish floats motionless 6.60 cm under the surface of the water.

a) What is the apparent depth of the fish when viewed at normal incidence to the water? Express your answer in centimeters. Use 1.33 for the index of refraction of water

b) What is the apparent depth of the reflection of the fish in the bottom of the tank when viewed at normal incidence? Express your answer in centimeters. Use 1.33 for the index of refraction of water.

Explanation / Answer

Refractive index of water = 1.33

(a)
The fish appears to be at a depth of:
6.60 / 1.33
=4.962 cm.

(b)
The mirror appears to be at a depth of:
19.1 / 1.33
= 14.36 cm.

The image of the fish appears to be:
14.36 - 4.96
= 9.4 cm. behind the mirror, giving it an apparent depth of:
14.36 + 9.4
= 23.76 cm.

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