Hands-on brainteaser: mirror reflections

Law of reflection

The important thing to know about mirrors is that a ray of light shining on a mirror at an angle will reflect off the mirror at the same angle - rather like a snooker ball bounces off a cushion.

In physics we say that the angle of incidence equals the angle of reflection. This is known as the law of reflection.

Standing in front of a mirror, some of the light bouncing off you hits the mirror and then bounces into your eyes.

That can be a bit hard to think about, so let's reverse the process: follow the light backwards from your eyes on to the mirror and then back on to you. This is what we call a line of sight.

Bathrooms and belly buttons

Imagine looking in the bathroom mirror and seeing yourself as far down as your belly button. Below your belly button is the bottom of the mirror and then just bathroom wall.

The line of sight goes from your eye to the bottom of the mirror, and then back on to your belly button.

You know from the law of reflection that when the line of sight reflects off the mirror, the angle of incidence equals the angle of reflection.

Another way of thinking of that is that the ray makes the two equal sides of an isosceles triangle, with your body as the third side.

Lines of sight

Click for larger image

Even through a telescope

• You can see from your belly button upwards because the bottom of the mirror (the tip of the triangle) happens to be at a height exactly half way between your eye and your belly button.

• That holds true as long as you don't move up or down - however far away you are from the mirror.

• Even if you look at the mirror through a telescope, you still won't be able to see what is below your belly button!

The key to Dallas' question is that the mirror must be vertical. Things are different if the mirror is tilted up or down. You might want to work out what happens there - you have all the physics you need.