question_answer

Keeping the incident ray constant, if a plane mirror is rotated through an angle \[\theta \], about an axis lying in its plane, then the reflected ray turns through an angle ________.

Answer:

Let the initial angle of incidence be\[x.\text{ }{{M}_{1}}\]and \[{{M}_{2}}\]are the initial and final positions of the mirror.\[{{N}_{1}}\]and\[{{N}_{2}}\]re the initial and final positions of the normal. AO is the incident ray, OB is reflected ray before rotation and OC is the reflected ray after rotation. We need to find the angle through which the reflected ray rotates i.e.,\[\angle BOC.\] By solving, we get \[\angle BOC=2\theta .\]