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# hw12sols - MasteringPhysics 2:22 PM Assignment Display Mode...

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5/8/08 2:22 PM MasteringPhysics Page 1 of 10 http://session.masteringphysics.com/myct Assignment Display Mode: View Printable Answers Physics 202 Assignment 12 Due at 11:00pm on Wednesday, April 23, 2008 View Grading Details Geometry and Reflections Description: A case of reflection from multiple surfaces, basically a geometry review. Learning Goal: To learn and practice the geometry skills necessary for complex reflection setups. The law of reflection has the very simple form , where is the angle between the normal and the incident ray and is the angle between the normal and the reflected ray. Although the law itself is easy to use, many realistic situations involve successive reflections from multiple surfaces. The law of reflection does not become any more complicated in such cases, but the geometry of the rays does become complicated. Consider the case of light shining onto a mirror, which is attached to another mirror at some angle , as shown in the figure . In this problem, we will find the angle at which light leaves the arrangement of two mirrors. Part A If the light strikes the first mirror at an angle , what is the reflected angle ? Express your answer in terms of . ANSWER: = Part B Now, find the angle (shown in the new figure ) in terms of . You can easily find in terms of , then just substitute your expression from Part A. Hint B.1 Relationship between and and are complementary angles. Express your answer in degrees in terms of . Notice that the degrees symbol is already listed for you, so just use the number "23" to indicate 23 degrees. ANSWER: = [ P

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5/8/08 2:22 PM MasteringPhysics Page 2 of 10 http://session.masteringphysics.com/myct Part C Now, find the angle shown in the figure in terms of and . Hint C.1 Angles in a triangle The sum of the angles in a triangle is . Express your answer in degrees in terms of and . ANSWER: = Part D Find the angle shown in the figure in terms of and . You will need to assume that , as it appears in the picture. Hint D.1 Relationship between and and are complementary angles. Hint D.2 How to find in terms of You can find in terms of by using the law of reflection. Express your answer in degrees in terms of and . ANSWER: = Virtually any reflection problem, no matter how intimidating it may seem, can be broken down into simple parts by considering each individual reflection carefully. Is Light Reflected or Refracted? Description: Mostly conceptual questions on index of refraction and Snell's law. Last few parts deal with total internal reflection. When light propagates through two adjacent materials that have different optical properties, some interesting phenomena occur at the interface separating the two materials. For example, consider a ray of light that travels from air into the water of a lake. As the ray strikes the air-water interface (the surface of the lake), it is partly reflected back into the air and partly refracted or transmitted into the water. This explains why on the surface of a lake sometimes you see the reflection of the surrounding landscape and other times the underwater vegetation.
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