The Secret Behind 5 Mirror Images — Revealed by Ray Optics Simulation!
I’m Ken Kuwako, a science trainer. Every day is an experiment.
Have you ever seen two mirrors facing each other in a hair salon or a fitting room? When you stand between them, your reflection seems to stretch endlessly into the distance, getting smaller and smaller. It’s a fascinating sight—but did you know that this phenomenon can actually be explained by a clear mathematical rule?
This time, while exploring how many images are formed between facing mirrors and how light travels as it reflects, I came across an excellent simulation website called Ray Optics Simulation. I’d like to introduce it and take you on a little journey into the fascinating world inside mirrors.
What happens when the mirrors are at 90°?
Let’s start with a familiar angle: 90°. If you place an object between two mirrors opened at a right angle, you can see 3 images, including the actual object. The most interesting one is the image furthest back. The light reaching this image has actually been reflected by the mirrors twice before it reaches our eyes.
In other words, the reflection we see furthest away isn’t produced by light that simply bounces off a mirror once. The light may bounce two, three, or even more times before finally reaching our eyes. It’s almost as if the light is going on a little “journey” inside the mirrors.
The magic formula for calculating the number of images
There is actually a simple formula for figuring out how many images are formed. If the angle between the two mirrors is θ, the number of images, n, can be calculated as follows.
n = 360°/θ – 1
For example, when the angle is 90°, we get 360 ÷ 90 – 1 = 3, which matches the 3 images we just saw. Using this formula, we can predict in advance how many images will appear for mirrors set at almost any angle.
What happens with mirrors at 60°?
Now let’s make the angle a little smaller and set it to 60°. Since 360 ÷ 60 – 1 = 5, we can see 5 images.
Now take a closer look at the third image counting outward from the real object. We can think of the light reaching this image as having been reflected 3 times before returning to our eyes. The narrower the angle between the mirrors, the more times the light travels back and forth between them, creating images farther and farther away. It makes you want to see this relationship for yourself: the smaller the angle, the more reflections occur, and the more images are produced. That’s where the simulation website I introduced at the beginning comes in handy.
https://phydemo.app/ray-optics/jp/
Try moving the light rays around and experimenting with different paths. You’ll quickly notice something fascinating. No matter what angle the light enters from, it keeps bouncing between the mirrors—once, twice, three times, and so on—until it reaches a particular image.
As a result of all these reflections, the 5 images appear neatly lined up. The simulation also clearly shows that the image furthest away is formed after the light has been reflected 3 times.
What did the simulation teach us?
Being able to move the light rays around yourself and actually watch how the images are formed is both useful and fun. Instead of simply calculating “11 images” or “3 reflections” with a formula, seeing exactly how the light bounces back and forth makes the idea much easier to understand—and much more memorable.
Who would have thought that behind such an ordinary phenomenon as facing mirrors lies such a beautiful mathematical rule, along with a fascinating “journey” in which light repeatedly bounces from mirror to mirror? It’s a little mysterious, and pretty fun to think about. If you get the chance, why not use a couple of mirrors at home and take a peek into this fascinating world for yourself?
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