Two plane mirrors are inclined at an angle such that a ray...

Two plane mirrors are inclined at an angle such that a ray incident on a mirror undergoes a total deviation of $240^{\circ}$ after two reflections. The angle between mirrors. Also discuss the formation of image : (a) $60^{\circ}, 5$ (b) $5^{\circ}, 60$ (c) $45^{\circ}, 5$ (d) $30^{\circ}, 6$

Two plane mirrors are inclined at an angle such that a ray incident on a mirror undergoes a total deviation of $240^{\circ}$ after two reflections. The angle between mirrors. Also discuss the formation of image :
(a) $60^{\circ}, 5$
(b) $5^{\circ}, 60$
(c) $45^{\circ}, 5$
(d) $30^{\circ}, 6$

Key Concepts

Dihedral Mirror Systems and Multiple Imaging

A dihedral mirror system consists of two plane mirrors inclined at an angle with respect to each other. Such an arrangement leads to the formation of multiple images of an object because the light is reflected repeatedly between the mirrors. The number of images formed can often be calculated using a relation involving 360° and the mirror angle; for instance, if 360° divided by the mirror angle is even, one of the images may coincide with the object, reducing the count of distinct images.

Image Formation in Plane Mirrors

Image formation in a plane mirror occurs when light rays from an object reflect off the mirror, producing a virtual image that appears erect and laterally inverted. In systems involving multiple reflections by two mirrors, these images are arranged with certain symmetries determined by the angles between the mirrors, and their number and positions can be predicted based on the geometry of the mirror setup.

Law of Reflection

The law of reflection states that when a light ray strikes a smooth surface like a plane mirror, the angle of incidence is equal to the angle of reflection. This principle governs the change in direction that a ray undergoes upon reflection and is fundamental to analyzing the path of light in mirror systems.

Angle of Deviation in Multi?Reflection Systems

When a ray reflects successively from two plane mirrors, its overall change in direction—or deviation—is determined by the geometry of the mirror arrangement. In particular, for a dihedral mirror system, the final direction of the ray is related to the angle between the mirrors. In some configurations, the deviation can be expressed as the difference between 360° and twice the mirror angle, which allows one to determine the mirror inclination when the total deviation is known.

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