A silver coin lies on the bottom of a clear lake 5.5 m deep. The coin is 4 cm in

Question

A silver coin lies on the bottom of a clear lake 5.5 m deep. The coin is 4 cm in diameter. The index of refraction of the water is 1.33. You are standing at the end of a pier, and your eye is 1.8 m above the surface of the water. You look directly at a point on the water that is a horizontal distance 2.4 m away from your eye in order to see the coin at the bottom of the river.

a) At what angle of incidence from the normal to the water are you looking?
degrees

b) What is the angle of refraction?
degrees

c) How far away along the horizontal direction is the coin actually located from your eye?
m

Explanation / Answer

a)

tan theta = 2.4/1.8

so theta = arc tan (2.4/1.8) = 53.13 degrees

ans is 53.13 degrees

b)

1* sin 53.13 = 1.33* sin r

r = 36.98 degrees

ans is 36.98 degrees

c) tan r = x/5.5

x = 5.5* tan 36.98 = 4.14 m

so distance = 2.4 + x = 6.54 m

ans is 6.54 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.