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Quiz_5_sol

# Quiz_5_sol - surrounded by a cylindrical glass...

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Problem 1 A man has +3.8 D lenses to provide full correction of his farsightedness. His old lenses are +2.5 D. (a) What is the near point for his unaided eyes? (b) How far away from his eyes he must hold a paper to use his old lenses? Solution: (a) 3.8 = 1 / 0.25 + 1/ d i => d i = -5 m. (b) 2.5 = 1 / d o – 0.2 => d o = 37 cm Problem 2 Two rays A and B travel down a cylindrical optical fiber of diameter d = 75 μ m , length l = 1 .0 km , and index of refraction n 1 = 1.465. Ray A travels a straight path down the fiber’s axis, whereas ray B propagates down the fiber repeated reflections at the critical angle each time it impinges on the fiber’s boundary. Determine the extra time t it takes for ray B to travel down the entire fiber in comparison with ray A, assuming the fiber is
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Unformatted text preview: surrounded by a cylindrical glass “cladding” with index of refraction n 2 = 1.46. Solution: ∆ t = t B-t A = l B v-l A v = 1 v ( l A sin θ c-l A ) = n 1 l A c ( n 1 n 2-1) = 1.7 × 10-8 s Problem 3 A light ray is propagating in a crystal where its wavelength is 540 nm. It strikes the interior surface of the crystal with an angle of 34 o and emerges into the surrounding air at 76 o to the surface normal. Find (a) the light frequency and (b) its wavelength in air. Solution: The index of refraction of the crystal: 74 . 1 34 sin 76 sin 2 = = o o n . (a) Frequency of the light is f = cn 2 λ 2 = 3 .2 × 10 14 H z . (b) 1 = cf = 937 nm...
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