Cylindrical mirror images

It’s neither here nor there

Introduction

Look into a cylindrical mirror and you will see images of yourself and of objects around you. Locating these images is difficult and provides an excellent test of your understanding of images.

Material

• A large concave cylindrical mirror, at least 12” wide and high. You can make a cylindrical mirror by placing a 1/8” thick plastic mirror into boiling water, then bending it around a cylinder and allowing it to cool.
• Two rulers, pencils or straight dowels
• a brightly colored object
• two people

Assembly

Mount the cylindrical mirror so that it curves from right to left. For example, place it on the edge of a table.

To Do and Notice

Look at yourself in the mirror. Move close to the mirror and then far away.

Look at yourself in the mirror, close up and far away.

Blink one eye and observe which eye your image blinks. When you are close notice that the mirror behaves like a flat mirror at home. Further away the image flips right-to-left. At some in-between distance it is difficult to focus on the image.

Hold the brightly colored object in front of and near the surface of the mirror. Move it side-to-side,observe that the image follows the object. Move the object further away, keep moving it side-to-side, notice that at larger distances the image moves opposite the object.

Place the object far enough from the mirror so that its image moves opposite. Look at the image of the object can you tell where the image is located by just looking at it?
Have two people put their eyes at the same level and point a stick at the image of the object. Notice where the sticks cross. This is where the light that leaves the object crosses on its way to the eye.

Two people point sticks Light from the curved mirror crosses at the image of an object,
at one possible position where the image might be seen.

Have the observers look at the image from two different heights in the same vertical line. The lines will cross behind the mirror.

Observed from above and below the sticks Solid lines show the path of light from the object to the eye.
Dashed lines are the eye-brain perception of the paths. These produce a virtual image behind the mirror.

What’s Going On?

The eye and brain combine to take the ambiguous clues to the location of the image in a cylindrical mirror and create one image.

There is no single location for this image. Looking into the curve of the mirror, two eyes see a real image in front of the mirror, looking with the two eyes along the flat part of the mirror they see a virtual image behind the mirror. At in-between angles the eyes and brain have to synthesize a single image.

Etc

At one particular distance of the object in front of the mirror, the real image in front of the mirror and the virtual image behind the mirror have the same angular size, it thus becomes easy for the eye-brain to combine the images into one perception. This perceived image however has no single distance at which it is located.