Doubt & Answer Explanation

Answer Explanation

When angle is rotated through an angle , the reflected ray gets changed by an angle . It can be seen in the figure below.

In the first case the angle of incidence is a. And in the second figure, the mirror is rotated by angle b.




Now, in the first case , the angle of incidence is a. So, the angle of reflection will also be a. In second case, the angle of incidence become a+b. So, the angle of reflection from the new normal is also a+b. Now, since the mirror is rotated by an angle b, so its normal gets rotated by angle b. And, the reflected ray now makes an angle a+b from this normal so total angle deflected by the reflected ray is b+b = 2b.

You can look at it in another way as:

Initially, the angle between the incident ray and reflected ray was 2a. Now it is 2(a+b). So, the difference is 2(a+b) - 2a = 2b. This is the angle moved by relected ray since the incident ray did not move.