Question

When a light ray strikes a plane mirror at an angle of $15^{\circ}$ with the mirror, what will be the angle through which the ray gets deviated?

\[\begin{align}
  & A{{.15}^{\circ }} \\
 & B{{.30}^{\circ }} \\
 & C{{.75}^{\circ }} \\
 & D.\text{none of the above} \\
\end{align}\]

Answer 1

Hint: We know that a plane mirror is a flat mirror which is slivered on one side and thus it acts as a reflecting surface. The image of the reflected object is erect, virtual and is of the same size and shape as that of the object. Also the image is laterally inverted, i.e. left right inversion.

Formula used: $\theta=2i$

Complete step by step answer:
We know that light has a property called reflection, which is the change in direction of the incident light due to some medium. The medium is generally silvered to aid reflection.
However, there are a few properties of reflection like the angle of incidence $i$ made at between the medium at the is equal to the angle of reflection $r$ with respect to the medium, if and only if the surface is smooth and polished for example a mirror.
Suppose the ray passes through the medium in a straight line, it will make the same angle $i$ with respect to the medium. Then deviation $\theta$ is the measure of this light passing through the medium with respect to the reflected light ray. It is also given as $\theta=2i$
Here since the light ray strikes a plane mirror at an angle of $15^{\circ}$ with the mirror.

Then the angle of deviation is given as $\theta=2\times 15=30^{\circ}$

So, the correct answer is “Option B”.

Note: According to the law of reflection of light: the angle of incidence, the angle of reflection and the normal to the mirror all lie on the same plane. Also the angle of incidence of the light is equal to the angle of reflection of the light ray. As the name suggests, the normal makes $90^{\circ}$ to the surface of the medium.