Question

A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of ${300^\circ }$ . The number of observable image is:
A. 60
B. 12
C. 11
D. 5

Answer 1

In order to answer this question, first we will apply the formula that is used during the deviation to find the angle of inclination. And then we will apply the formula to find the number of images formed in terms of the found angle.

Formula used:
The formula of angle of deviation is,
$\text{Angle of deviation} = {360^\circ } - 2\theta$
Where, $\theta$ is the angle of inclination.

Complete answer:
As per the question- A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of ${300^\circ }$.Here, we have to find the number of observable image with respect to the given statement-
So, as we know that the formula during the deviation:-
$\therefore O = {360^\circ } - 2\theta$
where, $O$ is the deviation, i.e.. ${300^\circ }$

Now we will substitute the value of angle of deviation,
$\Rightarrow {300^\circ } = {360^\circ } - 2\theta \\\ \Rightarrow \theta = {30^\circ } \\\$
Now, we can find the number of images formed in the given circumstances by applying the formula of no. of images in terms of $\theta$ :
$\therefore n = (\dfrac{{{{360}^\circ }}}{\theta }) - 1$
where, $n$ is the number of formed images after the deviation of ray that is reflected successfully from two plane mirrors,
$\Rightarrow n = (\dfrac{{{{360}^\circ }}}{{{{30}^\circ }}}) - 1 \\\ \therefore n = 11$
Therefore, the number of images formed is 11.

Hence, the correct option is C.

Note: In the same plane as the incident ray, the reflected ray, and the normal to the point of reflection. All forms of reflecting surfaces are subject to the law of reflection. A virtual and erect image is always formed by a flat mirror. The image and object are at the same distance from the mirror. A plane mirror produces a laterally inverted picture.