A fisherman, 1.8m tall, stands at the edge of a lake, being watched by a suspici

Question

A fisherman, 1.8m tall, stands at the edge of a lake, being watched by a suspicious trout who is some distance from the fisherman in the horizontal direction and a distance 47cm below the surface of the water. Use 1.35 as the index of refraction for water.

What is the angle of incidence of the light from the top of the fisherman's head on the surface of the water if the light hits the water a horizontal distance 4.21m from the shore?

What is the angle of transmission of the light ray into the water?

At what angle from the vertical does the fish see the top of the fisherman

Explanation / Answer

Part A)

The angle of incidence is found from the tangent function

tan(angle) = 4.21/1.8

angle = 66.9o

Part B)

From Snell's Law

n1sin(i) = n2sin(r)

1(sin 66.9) = 1.35(sin r)

r = 42.9o

Part C)

This is the same as part A

66.9o

Part D)

We need the horizontal distance to the fish

tan(42.9) = x/.47

x = .437m

Total x = 4.21 + .437 = 4.65 m

Part E)

We need to add the two hypotenuses...

From the Pythagorean Theorem

(1.8)2 + (4.21)2 = c2

c = 4.58 m

(.47)2 + (.465)2 = c2

c = .661 m

Finally .661 + 4.58 = 5.24 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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