You are standing on the edge of a pond, your eyes are a height of 1.75 m above t

Question

You are standing on the edge of a pond, your eyes are a height of 1.75 m above the water, and looking at the water at an angle of 2 = 45.0° to the vertical as shown in the figure. You see a fish in the pond. The actual depth of the fish is dactual = 1.21 m. 

a) Calculate the time it takes for light to travel on the path from the fish to your eyes.

b) Calculate the time light would take on a straight-line path from the fish to your eyes. 

c) Calculate the time light would take on a path from the fish vertically upward to the water surface and then straight to your eyes. 

d) Calculate the time light would take on the straight-line path from the apparent location of the fish to your eyes. 

Explanation / Answer

The speed of light changes depending on the medium. The speed of light v is related to the index of refraction n . We have
n = c/v where c is the speed of light in vacuum.
Also index of refraction is related to angle of incidence 1 and angle of refraction 2 as 

n= sin(1) / sin(2)

These are the basis for solution. Now we can atempt to solve this proplem

a) Calculate the time it takes for light to travel on the path from the fish to your eyes.

the distance D1 from eyes to water in terms of 1  height h is   D1 = h/sin(1)  and since 1=90 - 2 

  D1 = h/sin(90 - 2)  also D2 = dactual /cos(1)  and   1=2   

for air the speed of light is close to c however for water  v= c/n = c/( sin(1) / sin(2)) 

v=  c sin(90 - 2)/( sin(1) 

ttotal= t1 + t2 = D1/c + D2/v 

b) Calculate the time light would take on a straight-line path from the fish to your eyes. 

In this case make use of dapperent  to find D3 =dapperent /cos(2) and the total time 

ttotal= t1 + t3 = D1/c + D3/c = ( h/sin(90 - 2) + dapperent /cos(2))/c

BRB

c) Calculate the time light would take on a path from the fish vertically upward to the water surface and then straight to your eyes. 

d) Calculate the time light would take on the straight-line path from the apparent location of the fish to your eyes. 

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