Sam is sitting in her fishing boat watching a trout swim below the surface. She guesses the apparent depth of the trout at 2.0m. She estimates that her eyes are about 1.0 m above the water's surface, and that the angle at which she's observing the trout is 45 degrees.

Question

b) Calculate the actual depth of the trout

I have calcualted the angle of incidence to be 32 degrees, but still have no idea how to figure out the depth. I have been trying for 2 hours since last night. I don't know what trig to use on this. Can you help please?

physics - bobpursley, Saturday, January 16, 2010 at 10:30am

So Real depth= apparent depth/ tan i

check my thinking.

physics - drwls, Saturday, January 16, 2010 at 10:30am 
The formula that you need is derived and presented here:

The object will appear at a shallower depth equal to the real depth divided by the refractive index of water.

physics - Sarah N H, Saturday, January 16, 2010 at 11:15am 
Bob: your website, when I rearrange the formula, would be real depth = X/tani...What is the 'x" in my problem?

DRWLS: I am solving for the actual depth, the apparent depth is given...do I still use your same formula?

Thankyou both

Damon · Answer

Sarah,
Draw the figure three of us have suggested carefully labeling all the angles as is done in the links that Bob Pursley and Dr WLS have given you. r = 45. i =32 if that is what you got. Then you can work on the triangles and figure it out.

Sarah N H · Answer

I have drawn them all, but just want to make sure that I should be dividing 2 metres into tan1 (which is 32, to give me a real depth of 3 metres. Can you please verify that?