The law of reflection is quite useful for mirrors and other flat, shiny surfaces. (This sort of reflection is called specular reflection). However, you've likely been told that when you look at something, you are seeing light reflected from the object that you are looking at. This is reflection of a different sort: diffuse reflection. In this problem, you will see how diffuse reflection actually arises from the same law of reflection that you are accustomed to for reflections from mirrors.

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Part A Consider a spotlight shining onto a horizontal mirror (Figure 1). If the light from the spotlight strikes the mirror at an angle , to the normal, what angle 0, to the normal would you expect for the reflected rays? Express your answer in terms of 0.. VO AE ? 0,- Oa This simple rule of reflection no longer seems to hold for diffuse reflection. Consider the same spotlight but now reflecting from the surface of a table (Figure 2). Unlike the light reflected from the mirror, the light reflected from the table seems to go in all directions. If it didn't, then you'd only be able to see tables when you were at a specific angle to the lights above youl To understand why the light reflects in all directions, you must first look at a slightly simpler problem. Consider a flat surface, inclined downward from the horizontal by an angle a (Figure 3). The red line represents the surface and the red dotted line indicates the normal to this surface (the normal line). The two blue dashed lines represent horizontal and vertical. The angle between the incoming ray and the vertical is .. Throughout this problem, assume that , is larger than a but smaller than 2a. (If you wish, you can determine the correct sign rules to generalize your results later.) Part B Find the angle 0, between the reflected ray and the vertical. Express the angle between the reflected ray and the vertical in terms of a and . ινα ΑΣφ ? 0, = Oa + 2d Part A Consider a spotlight shining onto a horizontal mirror (Figure 1). If the light from the spotlight strikes the mirror at an angle , to the normal, what angle 0, to the normal would you expect for the reflected rays? Express your answer in terms of 0.. VO AE ? 0,- Oa This simple rule of reflection no longer seems to hold for diffuse reflection. Consider the same spotlight but now reflecting from the surface of a table (Figure 2). Unlike the light reflected from the mirror, the light reflected from the table seems to go in all directions. If it didn't, then you'd only be able to see tables when you were at a specific angle to the lights above youl To understand why the light reflects in all directions, you must first look at a slightly simpler problem. Consider a flat surface, inclined downward from the horizontal by an angle a (Figure 3). The red line represents the surface and the red dotted line indicates the normal to this surface (the normal line). The two blue dashed lines represent horizontal and vertical. The angle between the incoming ray and the vertical is .. Throughout this problem, assume that , is larger than a but smaller than 2a. (If you wish, you can determine the correct sign rules to generalize your results later.) Part B Find the angle 0, between the reflected ray and the vertical. Express the angle between the reflected ray and the vertical in terms of a and . ινα ΑΣφ ? 0, = Oa + 2d

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