Question

You’re standing in waist-deep water with your eyes 0.52 m m above the surface. A fish is swimming 0.65 m below the surface. Your line of sight to the fish makes a 38 ∘ angle with the water’s surface. Part A How far (horizontally) from you is the fish? Express your answer to two significant figures and include the appropriate units. x x = nothing nothing

Answer 1

Let the rays to the fish strike the water a distance x1 horizontally from you where

tan38∘=0.52/x1

x1=0.52/tan38∘

=0.666m

The refractive index of water is n = 1.333

The angle of incidence is A=90-38 = 52∘

The angle of refraction is B where

nsinB=sinA

sinB = (sin52)/1.333

= 0.591

=> B=36.2∘

The rays to the fish make an angle of 90-36.2=53.8∘ with the surface of the water.

The fish is a distance x2 horizontally from the point where the rays strike the water.

tan53.8∘=0.65/x2

x2=0.65/tan53.8∘

=0.476m.

So the fish is x1+x2 = 1.1 m from you horizontally.