Total and Diffuse Reflection

The previous page stated that the angle of incidence always equals the angle of reflection.  This law applies whether the item reflecting is a ball on a tennis court, a ground ball bouncing along a baseball field, or light reflecting from a mirror or a wall.  It is a universal law.  Yet common experience tells us that a baseball sometimes takes an unexpected bounce straight up, and that a laser beam striking a classroom wall must be reflecting into a wide range of angles since the spot on the wall can be seen by the entire class.  This apparent contradiction is resolved once we understand the difference between total reflection and diffuse reflection.

Consider a beam of laser light striking a surface as shown in the figures to the left.  Each region of the beam is traveling in the same direction when the beam strikes the surface.
Figure A:  The entire beam is reflected in the same direction in total reflection.
  1. If the surface is smooth, the normal to the surface will point in the same direction at each point on the surface.  The normals at three different points on the horizontal surface are indicated by the dashed vertical lines.  As the beam strikes the surface, each region of the beam of light will produce the same angle of incidence.  The same angle of incidence means the same angle of reflection, so the entire beam will reflect together with an angle of reflection equal to the angle of incidence.  This uniform reflection is called total reflection.
Figure B:  The beam is scattered in all directions in diffuse reflection.
  1. If the surface is not smooth, the direction of the normal to the surface will vary from point to point.  Again, normals at three different points are illustrated.  While the entire incoming beam travels in the same direction, different regions of the beam will produce different angles of incidences due to the differing directions of the normals.  For the leftmost region, indicated by a green label, the angle of incidence is 74 degrees.  But the central, purple-labeled, beam produces an angle of incidence of only 43 degrees.  At each point, the law of reflection holds, so the different regions of the beam will reflect with equally diverse angles of reflection.  Thus the reflected light will scatter in all directions; this scattering of light upon reflection is called diffuse reflection

The fielder who missed the ground ball was not necessarily ignorant of the law of reflection.  Instead, the ball could have struck a rough region of the field.  The law of reflection still held, but the normal to the surface was not necessarily vertical.  Since the fielder's expectations were based on a horizontal surface, the direction the ball traveled was a surprise.  (Note:  this is not the only explanation for a fielder's error, but it is a possible explanation.)

Diffuse and total reflection, and their difference, are also crucial to the operation of CD-ROMs.  The module on optical storage addresses this dependence in more detail.

What happens if the light is transmitted through the surface rather than reflected? 
Move on to the next part of the module to find out!

Copyright © 1999-2004 Doris Jeanne Wagner and Rensselaer Polytechnic Institute.  All Rights Reserved.