If two mirrors are inclined at some angle and an object is...

If two mirrors are inclined at some angle and an object is placed between the mirrors and there are 7 images formed for an object. Then what is angle between the mirrors?
(a) $54^{\circ}$
(b) $50^{\circ}$
(c) $60^{\circ}$
(d) $64^{\circ}$

Key Concepts

Law of Reflection

This fundamental principle of optics states that when light rays strike a mirror, the angle of incidence is equal to the angle of reflection. It is the basic mechanism behind image formation in mirrors and ensures that images are produced with the correct orientation relative to the object.

Multiple Image Formation in Angled Mirrors

When two plane mirrors are arranged at an angle to each other, an object placed between them will be reflected back and forth, producing multiple images. The specific number of images depends on the angle between the mirrors and the relative position of the object, as the reflections effectively ‘rotate’ the object’s rays around a full circle.

Formula for the Number of Images

There is a well?known formula that relates the number of images (n) to the angle (?) between two mirrors. In many cases, if 360 divided by ? is an integer, then the number of images is given by n = 360/? ? 1 when the object is placed along the bisector, and n = 360/? if it is off the bisector and 360/? is odd. This formula links the geometry of the mirror setup with the count of distinct images formed.

Angular Relationships in Mirror Systems

Understanding how the full angular circle (360°) is partitioned by the angle between the mirrors is key to predicting image formation in these systems. The idea is that the mirror configuration leads to a series of rotations of the object’s ray pattern by multiples of the mirror angle, and the number of successive rotations before the pattern repeats determines the number of images observed.

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