How can we find the angle between two plane mirrors if the no. of images formed are given?

Hello!

If the number of images is `n`, then the angle `alpha` between mirrors is

`alpha = 360/(n + 1)`

(in degrees, or  `(2pi)/(n+1)`   in radians).

To show this, consider the picture attached for `n=5` and `alpha=60` degrees.

Here O is an object, the mirrors are blue and hatched, and the reflections of mirrors are also blue. Five images are red dots and the real beam paths also drawn in red. The continuations of...

Hello!

If the number of images is `n`, then the angle `alpha` between mirrors is

`alpha = 360/(n + 1)`

(in degrees, or  `(2pi)/(n+1)`   in radians).

To show this, consider the picture attached for `n=5` and `alpha=60` degrees.

Here O is an object, the mirrors are blue and hatched, and the reflections of mirrors are also blue. Five images are red dots and the real beam paths also drawn in red. The continuations of beams are red and dotted.

The images 1 and 2 are formed with the help of one reflection. It is simple to find their positions: first take a perpendicular to a mirror going through an object. Then measure the distance from an object to the mirror and measure out the same distance to the opposite side of a mirror.

The images 3 and 4 require two reflections, from one mirror and then from the other. The beam path for the image 4 is shown. This image may be found as the reflection of the image 1 from the second mirror.

You can now draw a similar path for the image 3, and the image 5 requires even more reflections.