Two plane mirrors are inclined to each other such that an object placed between them has 11 images. Determine the angle of inclination

Analyze the question Two plane mirrors inclined at an angle θ form multiple images of an object placed between them. We are given the number of images (n = 11) and must find θ.

Concept The number of images formed is:

n = (360°/θ) − 1

This formula works when 360°/θ is an even integer (or when the object is on the bisector).

Solution 11 = (360°/θ) − 1

360°/θ = 12

θ = 360°/12 = 30°

Check with the other options

• 45°: n = 8 − 1 = 7
• 60°: n = 6 − 1 = 5
• 90°: n = 4 − 1 = 3

Tip Quickly memorize: 90° → 3 images, 60° → 5, 45° → 7, 30° → 11. Parallel mirrors (θ = 0) give infinite images. Always remember to subtract 1 from 360°/θ, because one of the "positions" is the object itself.