Question

For what angle between two plane mirrors,a light ray,after reflection once from each of the mirrors becomes parallel to the incident ray direction

Answer 1

see diagram.

incident and reflected rays are parallel if   2a+2b = 180 deg.=>   a+b=90 deg.angles DOE+ ODE+DEO = 180 deg90-a + 2c + 90-b = 180 deg     =>   c = 45 deg.angle between mirrors  = 2c = 90 deg.