Question

Keeping the incident ray constant if we rotate plane mirror through an angle (theta) then the reflected ray deviates in the same direction of rotation of mirror through an angle (2*theta). Explain it using a diagram. Please.

Answer 1

consider a mirror. initially let a ray be incident on the mirror at an angle \[\theta \] then the angle of reflection is also\[\theta \]
now let the mirror be rotated by an angle \[\phi \] the angle of incidence becomes \[\theta+\phi \]. the normal gets shifted by an angle \[\phi \]the angle of reflection is same as angle of incidence(\[\theta+\phi \] if initially the normal was at point A, the angle difference between old position of normal and new angle of reflection=\[\theta+\phi+\phi=\theta+2\phi \]now though mirror has been shifted through \[\phi \], the difference of angle between old and new angle of reflection =\[\theta+2\phi-\theta=2\phi \]
thus, even though the normal(mirror) has been shifted through angle phi, the reflected ray gets shifted through 2*phi.
B=new normal.