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Old Nov 23rd 2010, 07:43 AM   #1
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Reflection Problem When Diving

"At what angle to the surface must a submerged diver in a lake look toward the surface to see the setting sun just along the horizon?"

So once the angle of incidence hits the water, it gets refracted down forming a smaller angle than the angle of incidence. But is there a formula you can use to find the actual angle that the diver must look at to see the sun?
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Old Nov 24th 2010, 11:28 PM   #2
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Use:

(sin i)/(sin r) = 1.33

where i is the incident angle,
r is the refracted angle that you are looking for
1.33 is the refractive index of water.

I assume that there is no total internal reflection involved... and that the sun is taken to be at 90 degrees.
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Old Nov 27th 2010, 06:33 PM   #3
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Originally Posted by Unknown008 View Post
Use:

(sin i)/(sin r) = 1.33

where i is the incident angle,
r is the refracted angle that you are looking for
1.33 is the refractive index of water.

I assume that there is no total internal reflection involved... and that the sun is taken to be at 90 degrees.
Okay so then to do the math for this problem it would be

Sin i/sin r = 1.33
sin 90 = 1.33 sin r
sin 90/1.33= sin r which is .75?
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Old Nov 28th 2010, 09:56 AM   #4
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Yes, this is the value of sin r.

Find r now.
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Old Nov 28th 2010, 10:51 AM   #5
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Originally Posted by Unknown008 View Post
Yes, this is the value of sin r.

Find r now.
So then sin .75= .01? So then the angle is .01?
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Old Nov 28th 2010, 10:57 AM   #6
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No. Have you learned arcsine or sine inverse?

If

sin (x) = y

Then

x = sin^(-1) (y)

or

x = arcsin (y)
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Old Nov 29th 2010, 06:43 AM   #7
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Originally Posted by Unknown008 View Post
No. Have you learned arcsine or sine inverse?

If

sin (x) = y

Then

x = sin^(-1) (y)

or

x = arcsin (y)
Ahh i gotcha, so it would be 48.6 then correct?
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Old Nov 29th 2010, 07:27 AM   #8
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Yes! That's right!
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Old Feb 9th 2011, 07:27 PM   #9
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Originally Posted by Unknown008 View Post
Yes! That's right!
Could you explain why you assume that the sun is at 90 degrees? Is it 90 degrees to the normal?
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Old Feb 9th 2011, 10:01 PM   #10
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Yes, because when the sum sets, it's at level ground, hence, at 90 degrees to the normal
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