A scuba diver uses his waterproof flashlight to shine a beam of light so that it strikes the surface of the water at an angle of incidence theta i. Use Snell's law to find the angle of incidence that would give an angle of refraction for the refracted ray to be directed right along the surface, and show that theta i is the same as the critical angle for total internal refraction.

Any guesses anyone?

Question

A scuba diver uses his waterproof flashlight to shine a beam of light so that it strikes the surface of the water at an angle of incidence theta i. Use Snell's law to find the angle of incidence that would give an angle of refraction for the refracted ray to be directed right along the surface, and show that theta i is the same as the critical angle for total internal refraction. 

Any guesses anyone?

eturpin1 · Answer

@matt101 could you help me with this one?

matt101 · Answer

Sure! First let's look at a picture, because that will probably clear things up a bit for you.

The scuba diver is shining a light from INSIDE the water towards the surface where there's air. In other words, the light is moving from a a medium with a higher refractive index (n) to a lower refractive index. This means that when the light passes from the water to the air, it will bend AWAY from the normal. We're looking for that angle of incidence that bends the light so far away from the normal that it's actually parallel to the surface of the water:

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matt101 · Answer

What would Snell's Law be for this situation?

eturpin1 · Answer

$$n _{1}\sin \theta _{1} = n _{2}\sin \theta _{2}$$

eturpin1 · Answer

would this be correct?

matt101 · Answer

Yes - but you can simplify the equation a bit. Think about what θr is equal to!

eturpin1 · Answer

thanks so much!! I got it from here!