Multiple Mirrors

In this section we will deal with what happens when two mirrors are used, placed at angles to one another. We begin by considering two mirrors placed at right angles to one another.

We put an object (the small circle) inside the area bounded by two plane mirrors placed at right angles. How many images will the observer (eye) see of the object? Where will they be? How did the light go from the object to the observer in order to create these images? How many images will be seen if the angle is changed?

At the least, an image will be formed behind each mirror as we saw in the section on plane mirrors. The images will be as far behind each mirror as the object is in front. For the observer, the paths that light takes from the object to the mirror to his/her eye is also shown.

Imagine now that the right-hand mirror is extended, and you are able to see a reflection of image 1 in this extended mirror. This would give rise to image 3. Note that we can see things that are not immediately in front of a mirror if the angle that light takes is able to strike the mirror and bounce into our eye.

We could just as well have seen a reflection of image 2 in an extension of the upper mirror as shown here.

But how would the light rays get to the observer from the object that would enable him/her to see our image 3?

The light has to bounce twice in order to get from the object to our eye. Thus, image 3 is formed from a double bounce!

Is there anything different about image 3 when it is compared to images 1 and 2? One could argue that if image 1 is reversed front-to-back, and if image 3 is an image of 2, it should be re-reversed and end up correctly positioned front-to-back, top to bottom, etc. Check it out! All you need is to go to a department store and go to a dressing room area that has two right-angled mirrors. Notice that your third image doesn't look quite right. Yes, it's really how others see you not the image you're used to seeing in a mirror.



How many images would be formed by two plane mirrors placed at an angle of 45o?

The answer is 7 There is the original object, and then 7 copies or images of it. Notice how the mirrors get reflected, too, and form images of themselves.

So how many images will you get if you put the mirrors at a 60o angle? At a 30o angle?

So, is there a pattern? What is it? This is an excellent and easy lab to do, and can be done with relatively simple equipment.


As a result of this inquiry, you should have gotten some idea of how kaleidoscopes work, with two angled mirrors creating multiple images of colored glass and paper. See, it wasn't so bad after all!


There's even more to add to this section which will be forthcoming in future editions.

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