The Half-Height Secret: The Physics Trick That Lets Any Mirror Reflect Your Entire Body

Unlocking the Mirror Mystery: Why Half Your Height Is All You Need

I’m Kuwako Ken, your Science Trainer. Every day is an experiment.

When you head to the furniture store looking for a full-length mirror for your fashion check, do you find yourself searching for one that’s exactly the same height as you?

Here’s a secret: You absolutely don’t need a mirror that matches your height to see your entire reflection. It’s often written in textbooks, but theoretically, a mirror that is only “half your height” is sufficient to reflect your body from the top of your head to the tip of your toes.

“Wait, really? I know you can see everything if you stand far away, but not up close, right?” Many students feel this way. While it certainly seems counterintuitive when you try it, the geometric proof explains the phenomenon perfectly, bringing clarity to the confusion. This time, I’ve created a printable diagram that makes the mechanism immediately understandable.

Solving the Half-Height Puzzle with a Geometric Diagram

Here is the worksheet data you can use in class. Students are asked to determine the necessary range on the mirror (the line on the left) for the entire body of the person standing on the right to be reflected, specifically from their eye level.

Following the Path of Light Reveals the Secret

This is the answer key after completing the geometric construction.

The key to understanding this is the Law of Reflection.

How your head is visible: Light emitted from the top of your head reflects off the mirror and reaches your eye.

How your feet are visible: Light emitted from your toes reflects off the mirror and reaches your eye.

By drawing these light paths, we can see that the required mirror segment spans from the point halfway between your eye and the top of your head to the point halfway between your eye and your toes. When these two segments are added together, the total length is exactly half of your height.

It’s a simple diagram, but actually using a ruler to draw the lines—rather than just listening to a blackboard explanation—leads to a dramatic increase in student comprehension. The moment they realize, “Ah! It really is half!” is priceless. This is a point that requires careful explanation for students to fully grasp, so please feel free to use this worksheet!

[Science Side Note] Do you need an even smaller mirror if you step back?

Here’s another great question that often comes up from sharp students: “Sensei, if I step farther away from the mirror, won’t a smaller mirror be able to show my whole body?”

When you take a photo with a camera or a smartphone, the farther you move back, the wider the area you capture, right? It’s natural to assume a mirror works the same way.

However, the answer is a firm “NO”.

This “half-your-height” rule is constant, regardless of your distance from the mirror. If you move away, your reflection appears smaller, but at the same time, the section of the mirror needed to reflect your image also becomes narrower, meaning the ratio never changes.

“Whether you’re close or far, you always need half your height.” That is the fascinating and quirky nature of mirrors. If you have an accessible mirror at home, try covering the top and bottom with paper to create a “half-sized” mirror, and experiment by moving closer and farther away. You’re sure to experience a wonderfully strange sensation!

Inquiries and Requests

Bring the wonders and fun of science closer to home! We’ve compiled easy-to-understand tips and fun science experiments you can do at home. Feel free to search around!

The content of our science notebook has been published as a book. Find out more here

For information on the administrator, Kuwako Ken, click here

For various requests (writing, lectures, science classes, TV supervision, appearances, etc.), click here * Updates on articles are available on X!

The Science Trick Channel delivers experiment videos!