A cylindrically shaped jar is 5.5 cm in diameter and 3 cm tall. When an observer

Question

A cylindrically shaped jar is 5.5 cm in diameter and 3 cm tall. When an observer's eye is placed as shown, the observer sees the edge of the bottom of the empty jar. When the jar is filled with an unknown clear liquid, the observer (with his eye at the same position) sees the center of the bottom of the jar. Find the index of refraction of the liquid.

a) 1.27

b) 1.34

c) 1.30

d) 1.39

e) 1.44

A cylindrically shaped jar is 5.5 cm in diameter and 3 cm tall. When an observer's eye is placed as shown, the observer sees the edge of the bottom of the empty jar. When the jar is filled with an unknown clear liquid, the observer (with his eye at the same position) sees the center of the bottom of the jar. Find the index of refraction of the liquid. a) 1.27 b) 1.34 c) 1.30 d) 1.39 e) 1.44

Explanation / Answer

The angle of incidence is

Ai = Arctan(5.5/3)

Ai = 61.38 degrees

The angle of refraction is

Ar = Arctan [(5.5/2) / 3]

Ar = 42.51 degrees

Thus, as

n1 sin Ai = n2 sin Ar

And n1 = 1, solving for n2,

n2 = 1.30   [ANSWER, OPTION C]

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