The physical laws for reflection in a mirror are that (A) The reflected light ray is in the same plane as the incoming ray and the normal to the mirror. (B) The angle between the reflected ray and the normal to the mirror (the angle of reflection) is the same as that between the incoming ray and the normal to the mirror (the angle of incidence). This is usually stated as "the angle of reflection is equal to the angle of incidence". For a plane mirror, these laws are mathematically expressed by the formula ar = -a; + 2(a; . n)n, where n is a unit normal to the plane of the mirror, a; is the unit vector pointing in the opposite direction of the incoming ray and a, is a vector pointing in the direction of the reflected ray. 1. Sketch the vectors and label the angles. 2. Show that ar is also a unit vector. 3. Show that the formula above follows the two physical laws. For the first physical law you can do this with a couple of sentences or alternatively using appropriate dot and cross products. For the second, you should calculate an appropriate dot product to find an expression involving the angle of reflection and hence show that it is equal to the angle of incidence