# An underwater diver sees the sun 43° above horizontal. How high is the sun above the horizon to a fisherman?

+1 vote

An underwater diver sees the sun 43° above horizontal. How high is the sun above the horizon to a fisherman?

An underwater diver sees the sun 43° above horizontal. How high is the sun above the horizon to a fisherman in a boat above the diver?

~~~~~~~~~~

I tried doing the whole n1 sinX1 = n2 sinX2

and got (1.33)(sin 43) = (1.00)(sin X) so the answer I got was 65.102 degrees, but apparently that's not correct.

So then figured maybe I was using the wrong angle. So I tried:

(1.33)(sin (45-3)) = (1.00)(sin (45-x)) and got x=2.6604

Can anyone help me figure what I'm doing wrong and/or point me in the right direction? Am I using the proper equation?

## 2 Answers

+1 vote
by

Best answer

You got close.

The angles in the equation are not the angles relative to the horizon but are relative to the "normal" (The line that is perpendicular to the surface)

The angle under the water is 90-42 = 47.

n1 for water is 1.33, n2 for air is 1 Which you seem to understand.

(1.33)(sin (47)) = (1.00)(sin (x2))

Solving for x2= 76.58 degrees. But remember that that is the angle relative to the normal so you have to subtract it from 90 to get the angle relative to the horizon.

and you get 13.4 degrees.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.
0 votes
by

Underwater Diver

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.

+1 vote
2 answers
0 votes
1 answer
0 votes
1 answer
0 votes
1 answer
0 votes
3 answers
0 votes
1 answer
0 votes
3 answers
0 votes
1 answer
0 votes
2 answers
0 votes
2 answers