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6_prelab_solutions - Geometric Optics Solutions 1 1.1...

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Geometric Optics Solutions 1 1.1 Plexiglass has an index of refraction n = 1 . 49 . What is the speed of light in plexiglass? Equation 30.2 in your textbook states that the speed of light v in a medium with in- dex of refraction n is v = c n where c is the speed of light in a vacuum, c = 3 . 00 · 10 8 m s This gives v = c n = 3 . 00 1 . 49 · 10 8 m s v = 2 . 01 · 10 8 m s 1.2 At what angle of incidence does one expect total internal reflection? The light is inside the plexiglass and is traveling towards the interface between plexiglass and air. The index of refraction of the plexiglass is n 1 = 1 . 49. The index of refraction of air is n 2 and is given in your textbook, section 30.2. Snell’s Law states that n 1 sin θ 1 = n 2 sin θ 2 Total internal reflection first occurs when the angle of incidence is equal to the crit- ical angle, θ 1 = θ c . When total internal reflection occurs, no light will emerge from the 1
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plexiglass. In other words, the light is refracted at an angle θ 2 = 90 . The light skims along the interface between the two media, and never emerges. sin θ 2 = sin 90 = 1 In this special case Snell’s Law becomes n 1 sin θ c = n 2 sin θ 2 = n 2 Thus the critical angle θ c is sin θ c = n 2 n 1 (This is equation 30.5 in your textbook.) sin θ c = n 2 n 1 = 1 . 00 1 . 49
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