Image formation at angled Mirrors

When two mirrors are placed a various angles w.r.t each other, the light gets reflected over and over again it forms, multiple images.

Let M1 and M2 be 2 mirrors. Object O is the object.

If of angle between the mirrors is  90 degrees : Three images are formed. (Case i)

• Image I1 of Object O due to Mirror M1 is formed
• Image I2 of Object O due to Mirror M2 is formed
• Now Object is I2 and I1. The image of I1 is formed at position I3 due to mirror M1. The image of I2 is formed at position I3 due to mirror M2.

If  the angle between the mirrors is 0 degrees ie mirrors being parallel to each other: Infinite images are formed.(Case ii)

• Image I1 of Object O due to Mirror M1 is formed
• Image I2 of Object O due to Mirror M2 is formed
• Now Object is I2 and I1. The image of I1 is formed at position I3 due to mirror M2. The image of I2 is formed at position I4 due to mirror M1.
• Now Object is I3 and I4. The image of I3 is formed at position I5 due to mirror M2. The image of I4 is formed at position I6 due to mirror M1. And it continues...

Going by this, as the angle decreases from 90 to 0, the number of images keeps increasing. Recall the case of a Kaleidoscope wherein the angle between the mirrors is 60 degrees. So, many images(>3, 3 images are formed for 90 degrees) are formed.

Periscope: Periscope is an example wherein mirrors are placed at 45 degrees w.r.t each other.

• The light from the object is incident on the mirror M1 at an angle of 45 degrees.
• The light is reflected away from the mirror M1 at an angle of 45 degrees.
• It is again incident on mirror M2 at the same angle 45 degrees.
• Mirror M2 reflects it back to your eye at the same angle.

Periscopes are commonly used in submarines and military mainly for spying that is for observation from concealed positions. For a submarine which is deep inside the water, the surface and the objects above cannot be seen otherwise. But, by fitting a periscope, objects on the surface and outside can be viewed inside the submarine