Optics [refraction] - What is the actual angle from the surface of the water

Paulo Serrano

1. The problem statement, all variables and given/known data



The apparent angle from the water is 53 degrees, but what is the actual angle from the water?

2. Relevant equations

n1 * sin i = n2 * sin r

3. The attempt at a solution

I think the real problem here is I'm not seeing some basic geometry stuff. The answer is 37 degrees.

kuruman

Which angle in the drawing is "the actual angle from the water"? How is it defined? Does it help to point out the numerological result that 53^o+37^o=90^o?

Paulo Serrano

That "actual angle" is the angle from the horizontal line (the water line) and the red line representing the light from the lamp (the one that is smaller than 53 degrees).

And yeah, I guess it makes sense than 90-53=37, but why that is the right answer I do not know.

kuruman

OK, can you find the 53^o angle somewhere between the lines you have drawn below the surface of the water? Look at your drawing. The continuation of the lines that form the 53^o in air, form what angle on the other side? How is that related to the angle of refraction?

ehild

To help Kuruman, I modified your picture, showing the angle of incidence (i) and the angle of refraction (r). Look at the drawing, and find the value of r.

ehild

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