Page:Elementary Text-book of Physics (Anthony, 1897).djvu/419

 333. Law of Reflection.—In § 132 it is shown that when a wave passes from one medium into another where the particles constituting the wave move with greater or less facility, a wave is propagated back into the first medium. It is shown in § 133, that when the surface separating the two media is a plane surface, the centres of the incident and reflected waves are on the same perpendicular to the surface, and at equal distances on opposite sides. Considering the lines to which, as shown in § 325, the wave propagation in the case of light is restricted, a very simple law follows at once from this relation of the incident and reflected waves. In Fig. 98, $$C$$ and $$C'$$ represent the centres of the incident and reflected waves $$mn, on.$$ $$CA, AB$$ are the paths of the incident and reflected light. It will be evident from the figure that $$CA, AB$$ are in the same plane normal to the reflecting surface, and that they make equal angles with the normal $$AN.$$ $$CAN$$ is called the angle of incidence, and $$NAB$$ the angle of reflection. Hence we may state the law of reflection as follows: The angles of incidence and reflection are equal, and lie in the same plane normal to the reflecting surface. By constructing half-period elements in the reflecting surface, it can easily be shown that the portion of the wave from which light reaches $$B$$ is that lying around $$A.$$ This may likewise be shown by proving, as can easily be done, that light traverses the path $$CAB$$ from $$C$$ to $$B$$ which fulfils this law, in less time than it requires to traverse any other path by way of the reflecting surface.