Study this guide first:  Ray Tracing and Image Formation in Plane Mirrors.

Note: When asked to draw a sketch or diagram for an optics problem, a free-hand drawing is acceptable. When asked to make a construction, use a ruler (and protractor if needed), and construct lines and angles accurately and to scale.

1. Two plane mirrors are placed at right angles to each other as shown to the right. Light ray q is incident on Mirror 1 at angle θ_i1, reflects from that mirror at angle θ_r1, is incident on Mirror 2 at angle θ_i2, and reflects from that mirror at angle θ_r2. Prove using a logically-reasoned argument that rays q and r are parallel. Use known principles of geometry and optics in your proof. Present the steps of your proof clearly in a list format. Use the same symbols as in the given diagram; however, you may draw additional lines as you see fit.

2. Click here to open a template for the next problem. Print it in landscape orientation. You'll draw your construction on the print. The goal is to construct the image of the object arrow from the point of view of someone looking into the intersection of the mirrors (as opposed to just looking into one mirror or the other). One ray is already traced for you.  You need to draw three more rays that reflect from both mirrors. The green ray shown below wouldn't be helpful, because it reflects from only one mirror. The blue ray, however, will work. Here are some things to be mindful of as you make your construction.

   1. Use a straight edge and make sure that your incident and reflected rays obey the law of reflection.  If you're careful, you'll get good results.  However, a small deviation in angle can result in large errors.  In order to get the angles of incidence and reflection equal, count squares in the rise and run of a line as shown below. The bigger the distance you measure, the more accurate the resulting angles will be. You may also find the result that you proved in problem 1 to be useful.

   2.  Add arrowheads to the rays to indicate direction.

   3. When you extend reflected rays behind the mirror, line your straightedge up carefully with the reflected ray. The reflected ray that you extend backwards behind the mirror is the ray after reflection from both mirrors.

   4. Indicate the orientation of the image by putting an arrowhead on the correct end. This is the end that corresponds to rays drawn from the tip of the object arrow.

   5. When finished with the construction, tell whether the image is i) upright or inverted (compared to the object), ii) reduced, same size, or enlarged, iii) real or virtual.

Here's an interesting thing to test if you have two mirrors that you can hold at right angles. First try a single mirror. Hold your hand in front of the mirror and note how the orientation of your hand compares to its image. Then try the same thing with two mirrors at right angles. In this case, it's important to view from a position where you're looking into the intersection of the mirrors rather than at one mirror or the other. Another thing to try is to hold written material up to the mirrors. You'll be able to read it normally.

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