A ray of light strikes a plane mirror at an angle of 30 degrees. The mirror is rotated by 15 degrees. By how many degrees will the reflected ray...

As per the law of reflection, the angle of incidence (the angle made by an incident light ray with a normal to the surface) is equal to the angle of reflection (the angle made by the reflected light ray with the normal). In other words,

angle of incidence = angle of reflection

In this case, the incident beam makes an angle of 30 degrees. Then the angle made with the normal to the mirror surface is 60 degrees (= 90 - 30). Therefore, the angle of reflection is also 60 degrees. And the reflected ray will make an angle of 30 degrees (= 90 - 60) with the mirror.

Now, if the mirror is moved by 15 degrees towards the light ray, the light ray will now make an angle of 15 degrees (= 30 - 15) with the mirror. In this scenario, the angle of incidence and the reflection would be 75 degrees (= 90 - 15).

If the mirror were to be rotated away from the light ray, the new angle of incidence and reflection would be 45 degrees.

Therefore the reflected ray (and the angle of reflection) will also be rotated by 15 degrees, if the mirror is rotated by 15 degrees.

Hope this helps.