question_answer

The angle between an incident ray and reflected ray for a given reflection is x. If the mirror is rotated through an angle x/2, keeping the incident ray constant, then find the angle between incident ray and reflected ray after rotation. Consider both clock wise and anti-clock wise direction.

Answer:

The angle between the incident ray and reflected ray \[=x\Rightarrow i=r=x/2\] (i) After the mirror is rotated through an angle of\[x/2\]in clock wise rotation, then the new angle of incidence becomes\[3x/2\]and the new angle of reflection becomes\[3x/2\]. Therefore the angle between the incident ray and reflected ray                 = New angle of incidence + New angle of reflection\[=3x/2+3x/2=3x.\] (ii) After the mirror is rotated through an angle of\[x/2\]in anti clock wise rotation, then the new angle of incidence becomes\[x/2\]and the new angle of reflection becomes\[x/2\]. Therefore the angle between the incident ray and reflected ray = New angle of incidence + New angle of reflection \[=x/2+x/2=x.\]