A fish is 2.1 m beneath the surface of a still pond of water.At what maximum angle can the fish look toward the surface (measured with respect to the normal to the surface)in order to see a fisherman sitting on a distant bank? (for water,n = 1.333)
A) 18.6°
B) 48.6°
C) 37.2°
D) The fish will not see the fisherman at any angle.

Question

Quizplus · Accepted Answer

The maximum angle can be obtained using Snell's law:

n1*sin(theta1) = n2*sin(theta2)

where n1 and n2 are the indices of refraction for the initial and final media, theta1 is the angle of incidence (measured with respect to the normal to the surface), and theta2 is the angle of refraction.

Assuming that air is the initial medium (n1 = 1.00) and water is the final medium (n2 = 1.333):

sin(theta2) = (n1/n2)*sin(theta1)
sin(theta2) = (1.00/1.333)*sin(theta1)
sin(theta2) = 0.75*sin(theta1)

When the fish is looking at the surface, the light ray will travel from the fish to the surface, then from the surface to the fisherman. Therefore, the angle of incidence for the first refraction will be equal to the angle of refraction for the second refraction. That is,

theta1 = theta2

Substituting the expression for theta2 into the equation above:

sin(theta1) = 0.75*sin(theta1)
1 = 0.75

This is not possible, so the fish will not see the fisherman at any angle. Therefore, the answer is D.

A Fish Is 2