01 Confusing Mirrors (mirrors at 90 degrees)

Aim¶

To show just plane mirrors in which the images are rather complicated.

Subjects¶

• 6A10 (Reflection From Flat Surfaces)

Diagram¶

Equipment¶

• Planar mirror.

• Two hinged planar mirrors.

• Revolving double mirror; the mirrors stand perpendicular to each other.

• Three planar mirrors arranged as a corner cube. .

Presentation¶

1. Look into the planar mirror.

As is known very well,the image of the left hand is a right hand. But why are top and down not interchanged?.

2. Look into the hinged double mirror (see Figure 2), the angle between the two mirrors ( $\alpha$ is larger than $90^{\circ}$. Moving your eyes you see left and right an image of your head (Figure 2 A). Left/right is interchanged in the images.

Now make the $\alpha$ smaller than $90^{\circ}$. At around $\alpha=60^{\circ}$ you see four images (see Figure 2 B): The image in the left mirror is again imaged in the right mirror and viceversa.

Slowly the $\alpha$ is made smaller and the two imaged images fall together (at $\alpha=90^{\circ}$ ) (see Figure 2 C). Move your head on one side to observe this particular image and see that in this image left is still left.

3. Look at the revolving double mirror (see Figure 3 A). Turn it round slowly and observe that you are upside down (your image is rotated $180^{\circ}$ when the mirror.

4. Look (close one eye) into the arrangement of three planar mirrors (see Figure 4).

Observe:

• left remains left and up becomes down;

• your eye remains caught in the middle of the arrangement; it won’t help moving your head up-down/right-left.

Explanation¶

For explanation see the demonstration Corner cube.

Sources¶

• Hecht, Eugene, Optics, pag. 178-180 and 195

• Stewart, J, Calculus, pag. 791 and 796