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Two plane mirrors are at right angles to each other as shown by the side view in Figure P22.10. A light ray is incident on mirror 1 at an angle $\theta$ with the vertical. Using the law of reflection and geometry, show that after the ray is reflected off of both mirrors, the outgoing reflected ray is parallel to the incident ray.

$\begin{array}{l}{\text { Using the law of reflection and geometry, it is proved that the ray is reflected }} \\ {\text { off, the outgoing ray is parallel to the incident ray. }}\end{array}$

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Cornell University

University of Washington

Hope College

University of Winnipeg

we're told that we have two plane mirrors at right angles to one another and asked to look at figure p 22.10 as reference. So the light rays into a mere one angle, fatal with the vertical. So use the law of reflections and geometry to show that this rays reflected off both mirrors and the outgoing reflected rays parallel to the incident reflected. Right. Okay, So the angle of the incident on the Mir one estate, as we're told and by the law of reflection, the angle of incidence is England equal to the angle of reflection. Hence the angle of reflection at mirror one. We're gonna call this data. One is equal to Fada. Okay, Pretty simple. So far, so in the triangle than ABC on the image that some of the interior angles, of course, is going to be equal to 180 degrees. So from that figure, we have data one Plus, they did too. Plus, since it's a right, a right angle here, 90 degrees, all of this has to add up to 180 degrees. Okay, Okay. And since data one equal stated to excuse me since data one equal state of what we said at the very top. Right here, we can go ahead and sulfur data to In terms of data, we find that data to is equal to 90 degrees, minus data. So hence the angle of incident on near to which is stated to is 90 degrees minus data. So now again, by the law of reflection, the angle of incidence is equal to the angle of reflection. So the angle of reflection that mirror to data to is going to be equal to data three. So now we have 82 is equal to data three, which means that they had a three is equal to 90 degrees minus data. Right. So the angle the incident Ray makes with Mir one looking there at the image we're told is fine. And start a new page for this five is equal to 90 degrees minus data. And we're told that that is the angle of incident at mere one. And because if you look back on the equation, we just found for Data three. We found that it was also 90 degrees minus data. That means that the angle of incident on Mir one is equal to fate of three and data three is the outgoing reflected Ray from ear to. So we just proved that we were asked to show and we'll go ahead and just type it out here we can say. Thus outgoing reflected Ray from Mir two is parallel to the incident. Ray on mirror one. See if we can get all this in the No, There we go and we can box. I did as our solution to the question period in box it it