Question

if a plane mirror is shifted by an angle thita what will be the angle of reflection?

Answer 1

Angle of incidence = angle of reflection

Answer 2

So the angle between the incident and reflected ray is
\[ \alpha + \alpha = 2 \alpha \]

Now we rotate the plane mirror by angle theta (the rotation shown as the change in angle between the original normal, n, and the new normal, n'


When the mirror is shifted by an angle theta while holding the incident ray steady, the angle of incidence is still equal to the angle of reflection, therefor,
\[(\theta + \alpha) + (\theta + \alpha) = 2\theta + 2\alpha\]
The reflected ray gets rotated a total of 2 theta.

Measured from the original normal, if plane mirror is rotated an angle theta, the angle of reflection is
\[ 2\theta + \alpha\]