A laser pointer is located at (−1.0m,0.50m) in a rectangular laboratory room. A flat vertical mirror coincides with the plane x=0 from the floor (y=0) up to y=2.0m. A photo-detector target is fixed on the opposite wall at the point (3.0m,1.20m).
The laser beam must be aimed so that it reflects once from the mirror and then strikes the target.
(a) Determine the coordinate of the virtual image of the target formed by reflecting the actual target across the plane mirror.
(b) Derive the equation of the straight line that connects the laser pointer to the virtual image found in part (a).
(c) Calculate the exact (x,y) position on the mirror surface where the beam must strike so that, after reflection, it reaches the real target.
(d) Compute the numerical value of the angle that the incident beam makes with the normal to the mirror at the point of incidence, and verify that the reflected beam makes the same angle with that normal.