A light ray is incident on a horizontal plane mirror at an angle of 45^∘. At what angle should a

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A light ray is incident on a horizontal plane mirror at an...

A light ray is incident on a horizontal plane mirror at an angle of $45^{\circ}$. At what angle should a second plane mirror be placed in order that the reflected ray finally be reflected horizontally from the second mirror, as shown in figure: (a) $\theta=30^{\circ}$ (b) $\theta=24^{\circ}$ (c) $\theta=22.5^{\circ}$ (d) $\theta=67.5^{\circ}$

A light ray is incident on a horizontal plane mirror at an angle of $45^{\circ}$. At what angle should a second plane mirror be placed in order that the reflected ray finally be reflected horizontally from the second mirror, as shown in figure:
(a) $\theta=30^{\circ}$
(b) $\theta=24^{\circ}$
(c) $\theta=22.5^{\circ}$
(d) $\theta=67.5^{\circ}$

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Key Concepts

Law of Reflection

This principle states that when a light ray strikes a plane mirror, the angle of incidence (measured from the normal to the surface) is equal to the angle of reflection. It is a fundamental rule in optics that underpins the behavior of light as it interacts with reflective surfaces.

Geometric Analysis of Reflection

Analyzing reflections involves constructing diagrams with the incident ray, the reflected ray, and the normal to the mirror surface. This method allows one to apply the law of reflection and use geometric relationships to calculate unknown angles or determine the orientation of mirrors needed to achieve a desired light path.

Dual-Mirror Reflection Systems

In configurations involving two mirrors, the sequential reflections can be studied by considering how the orientation of the second mirror affects the path of the light after the first reflection. The cumulative effect of the reflections determines the final direction of the light beam, which is critical for designing optical devices that require precise control of light direction.

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