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Solutions to Homework Questions 8

Physics 112 **Homework** 8 (solutions) (2004 Fall)**Solutions** **to** **Homework** **Questions** 8Chapt22, Problem-6: The two mirrors in Figure P22.6 meetat a right angle. The beam of light in the vertical plane P strikes mirror 1 asshown. (a) Determine the distance the reflected light beam travels beforestriking mirror 2. (b) In what direction does the light beam travel after beingreflected from mirror 2?Solution:The first point **to** note here is that everything happens in a thedashed Plane P (only specular reflection need be considered). Thusit is possible (and useful) **to** redraw the geometry in only 2D(ie the situation as ‘seen’ in plane P).Once we have done that, the problem becomes one of ‘simple’trigonometry plus the law of reflection (applied twice – once ateach mirror).Mirror 2The 2D-view is shown right. So ….(a) Where we are asked for the distance d.Well we apply the law of reflection for mirror1, then given thedistance of that that reflection from mirror2, we can use simpletrig **to** calculate the distance requested1.25 m = d sin 40.0° , so d = 1.94 m.(b) Where we are asked for the direction following the 2 nd reflectionHere (again) using simple trig, we can calculate all the anglesassociated with the “angle of incidence” of the 2 nd reflection..Armed with this we simply apply the Law of Reflection again **to** obtain50.0° above horizontal , or parallel **to** the incident ray.40°50°i 2 = 50°d1.25 m40°i 1 = 40°50° 50°Mirror 1Chapt22, Problem-7: An underwater scuba diver sees the Sun at an apparent angle of 45.0° from the vertical.What is the actual direction of the Sun?Solution:Here one simply has **to** use Snell’s Law – obviously a sketch helps…n 1 sin ! 1 = n 2 sin ! 2sin ! 1 = 1.333 sin 45.0°sin ! 1 = (1.333)(0.707) = 0.943so ! 1 = 70.5° " 19.5° above the horizontaln 2 = 1.333! 1n 1 = 1.00! 21

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