Answer to Question #129274 in Optics for UCHENNA

Question

When a plane mirror on which a ray is incident is rotated through 100, the reflected ray is rotated through what angle

Answer 1

Let the initial angle of incident be $\angle AOB = \alpha$. Then the initial reflection angle also will be: $\angle EOA = \alpha$. Suppose we rotated the mirror by the angle $\angle AOC = \theta = 100 \degree$. Then, according to the figure, we need to fing the angle $\angle EOD$ - the angle between old and new reflected rays. It will be:

$$\angle EOD = \angle EOA + \angle AOB + \angle BOC + \angle COD$$

First two angles we've already known, so let's fihd the last two.

$$\angle BOC = \angle AOC - \angle AOB = \theta-\alpha = 100\degree-\alpha$$

As incident and reflection angles:

$$\angle COD = \angle BOC = 100\degree - \alpha$$

Thus, obtain:

$$\angle EOD = \alpha + \alpha + (100\degree - \alpha) + (100\degree - \alpha) = 200\degree$$

Answer. $200\degree$.