Question

Relaxing by the lake in the summer after finishing your physics class, you are standing on a pier, looking out over the water, recalling that light in water travels at only 75% of the speed it travels in air. You look down to see a fish resting at the bottom of the lake at a depth of 2 meters. If your eyes are 3 meters above the surface of the water and you are looking down at an angle of 30 degrees below horizontal, how far is the fish from the pier?

Answer 1

If fish is observed while looking down at an angle 30o with horizontal, then the emergent ray from water makes angle 60o with normal as shown in figure.

By law of refraction, sin( 60 ) / sin (r) = .....................(1)

where r is angle of incidence at water-air interface for the light ray coming from fish and is refractive index of water.

If light travels in water with 75% speed as it travels in air,

refractive index = speed of light in air / speed of light in water = c / 0.75 c = 4/3 = 1.333

Using the value of refractive index, we get sine of angle r as

sin (r) = sin(60) / = sin(60) / 1.333

we get angle r from above equation as , r = 40.5o

As seen from figure , fish is from observer at a distance ( AB + CD )

AB = 3 / tan30 = 5.196 m ; CD = 2 tan (40.5) = 1.708 m

Hence , fish is seen from observer at a distance 6.904 m