Question

light incident on a rotating mirror M is returned to a fixed mirror N placed 22.5 km away from M . the fixed mirror reflect it back to M (along the same path) which in turn reflect the light again along a direction that makes an angel of 27 degree with the incident direction. the speed of rotation of the mirror is

Answer 1

In 1st case,
angle of incidence =90 degree
so according to  the Law of Reflection "the angle of reflection is equal to the angle of incidence, and the incident ray, the reflectedray, and the normal to the surface at the point of incidence all lie in the same plane."
So the reflecting angle will be also 90 degree.
and the light ray will reflect back in the same path.

2nd case,
Now , When you tilt the mirror by  θ degree.
the normal to the surface will also tilt making an angle of θ degree with the incidence ray.
and the reflecting ray will also make an angle of θ degree with the normal to the mirror (according to the law of reflection).
Hence,
=>the angle between the incident ray and reflected ray = θ  + θ degree
=>the angle between the incident ray and reflected ray =  2θ degree