# HW19Sol - o angle we know that it reflects straight back...

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Jim Guinn’s PHYS2212 Assignment #19 Solutions 1. What is the Law of Reflection and what does it mean? The Law of Reflection states that θ i = θ r , or for an incident ray reflecting off of a flat mirror, the angle between the incident ray and the perpendicular to the surface ( θ i ) is equal to the angle between the reflected ray and the perpendicular to the surface ( θ r ) . 2. In the diagram to the right, an object (solid arrow) creates an image (dotted arrow). Show that the Law of Reflection implies that the object distance = image distance, that is, the distance from the object to the mirror is the same at the distance from the image to the mirror. (This is a simple geometric proof.) For a ray striking the mirror at a 90
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Unformatted text preview: o angle, we know that it reflects straight back. Tracing this ray behind the mirror, we see the image will be at the same height as the object. The image will form at a point where a general ray, when traced back, will cross this perpendicular line. From the diagram, we see that θ 1 = θ 2 from opposite internal angles, θ 2 = θ 3 from the Law of Reflection, θ 3 = θ 4 from crossing parallel lines, and so θ 1 = θ 4 . Since the length L is the same in the two triangles, and both have two equal angles, we know the triangles are congruent, and so the image must be at the same distance from the mirror as the object! Isn't physics wonderful?!?...
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