A person in a boat sees a fish in the water (n = 1.33),the light rays making an angle of 40$\degree$ relative to the water's surface.What is the true angle (in degrees)relative to the water's surface of the same rays when beneath the surface?

Question

Quizplus · Accepted Answer

The angle of incidence in air is equal to the angle of refraction in water (since the light rays are entering the water from air and not from any other medium). Therefore, the ray will make the same angle of 40 degrees with the normal (line perpendicular to the surface of the water) at the point of incidence on the water's surface.

Now, using Snell's law, we can find the angle of refraction at the interface of water and fish.

n1 sin(theta1) = n2 sin(theta2)

where n1 = refractive index of air = 1, 
n2 = refractive index of water = 1.33, 
theta1 = angle of incidence in air = 40 degrees

Substituting the values and solving for theta2,

theta2 = sin^(-1)((n1/n2) * sin(theta1))

theta2 = sin^(-1)((1/1.33) * sin(40))

theta2 = 30.7 degrees (approx)

Therefore, the true angle (in degrees) relative to the water's surface of the same rays when beneath the surface is

90 - theta2 = 90 - 30.7 = 59.3 degrees (approx)

Rounding off to the nearest whole number, we get 59 degrees, which is closest to option D) 55 degrees.

A Person in a Boat Sees a Fish in the Water