test3a_fall07

# test3a_fall07 - PHY 206 EXAM III Nov 14 2007 NAME SIGNATURE...

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PHY 206 EXAM III Nov. 14, 2007 NAME: SIGNATURE: ID: 1. 2. 3. Some relations you may need: n a sin θ a = n b sin θ b n a s + n b s 0 = n b - n a R 1 s + 1 s 0 = 1 f

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1. A scuba diver sets off a flash bulb a distance h below the surface of a lake (index of refraction n ). Observers floating in a boat see light transmitted through a circle on the surface, defined by the critical angle for total internal reflection, θ c . a) Find the radius R of this circle. b) Suppose a layer of oil, with thick- ness t and refractive index n 0 (1 < n 0 < n ), floats on the wa- ter above the flash. Now the light transmission circle for the boat observers is determined by the critical angle at the oil-air interface. Is the radius of the new circle larger, smaller or the same as in the absence of the oil? (You can answer this without computing the new radius directly by drawing a picture and arguing from Snell’s law.) h θ c θ c R n Solution: a) Snell’s law says, n sin θ c = 1, and the geometry of the right triangle formed by R , h , and θ c yields: sin θ c = R R 2 + h 2
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