A ray of light falls on a plane mirror. When the mirror is...

A ray of light falls on a plane mirror. When the mirror is turned, about an axis at right angle to the plane of the mirror through $20^{\circ}$, the angle between the incident ray and new reflected ray is $45^{\circ}$. The angle between the incident ray and original reflected ray is: (a) $15^{\circ}$ (b) $30^{\circ}$ (c) $45^{\circ}$ (d) $60^{\circ}$

A ray of light falls on a plane mirror. When the mirror is turned, about an axis at right angle to the plane of the mirror through $20^{\circ}$, the angle between the incident ray and new reflected ray is $45^{\circ}$. The angle between the incident ray and original reflected ray is:
(a) $15^{\circ}$
(b) $30^{\circ}$
(c) $45^{\circ}$
(d) $60^{\circ}$

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Key Concepts

Effect of Mirror Rotation on Reflected Ray

Rotating a plane mirror results in a change in the direction of the reflected ray. Specifically, when the mirror is rotated by a certain angle, the reflected ray rotates by twice that angle due to the geometry of reflection, which is crucial in analyzing changes in the ray’s path.

Geometric Relationship in Reflection

The calculation of angles between incident and reflected rays involves geometric construction, especially when the mirror's orientation changes. Understanding these relationships helps determine how changes in the mirror's alignment affect the overall angular disposition between the various rays.

Law of Reflection

This principle states that the angle of incidence is equal to the angle of reflection when a light ray strikes a surface. It forms the basis for understanding how light behaves when interacting with reflective surfaces like plane mirrors.

Plane Mirror Reflection

In plane mirror reflection, the reflected ray maintains the same angle with respect to the normal as the incident ray. This property gives rise to characteristics such as the formation of virtual images that are laterally inverted relative to the object.

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