Question

A catfish is 2.00 m below the surface of a smooth lake. (a) What is the diameter of the circle on the surface through which the fish can see the world outside the water? (b) If the fish descends, does the diameter of the circle increase, decrease, or remain the same?

Answer 1

Given that,

The cat fish is L = 2 m below the surface of the lake.

(a)we need to find the diameter of the circle through which the fish can see the world outside the water. Let ot be D.

Please refer to the attaced figure.

Let c be the angle at which the total internal reflections occurs. For this situation we can write:

n(water) x sinc = n(air)

sinc = [n(air)/n(water)]

we know that, n(water) = 1.33 and n(air) = 1

sinc = 1/1.33 = 0.7518

c = sin-1(0.7518) = 48.75 degrees

Now, tanc = R/L => R = tanc x L = tan(48.75) x 2 = 2.28 meters

D = 2 x R = 2 x 2.28 = 4.56 meters

Hence, the diameter of the circle = D = 4.56 meters.

(b)If the fish decends, the diameter will increase, as we just saw that,

D = 2 x R = 2 x tanc x L , where L is the deth, so it will increase with the increase of the depth.