Question

A plane mirror gives a spot of light on a screen which is 3m from the mirror. The screen is perpendicular to the initial direction of light. When the mirror is rotated, the spot light moves a distance of 4m across the screen. Calculate the angle of rotation of the mirror.

Answer 1

Answer:

$53.06^\circ$ is the angle of rotation of the mirror.

Explanation:

Given that

Distance between screen and plane mirror = 3m

Please refer to the attached image.

Let initial position of plane mirror be AB.

Light is perpendicular to it, i.e. OI be the light.

OI = 3m

Then the mirror is rotated such that the spot light moves 4m across the screen.

Let I' be the new point so, II' = 4m

We have to find the angle of rotation of mirror.

i.e. $\angle AOA' = ?$

We can clearly see from the figure that $\angle AOA' = \angle IOI'$

Let the angle be equal to $\theta$.

Using tangent trigonometric identity in $\triangle IOI' :$

$tan\theta = \dfrac{Perpendicular}{Base}$

$tan\theta = \dfrac{II'}{OI}\\\Rightarrow tan\theta = \dfrac{4}{3}\\\Rightarrow \theta = tan^{-1}(\dfrac{4}{3}) \\\Rightarrow \theta =53.06^\circ$

So, the answer is:

$53.06^\circ$ is the angle of rotation of the mirror.