Measuring Angles

On the Discussion Question page, the figure of the ball bouncing contained an angle θi.  This angle, called the angle of incidence, describes how the ball approaches the surface.  This angle is measured from the path of the ball to the normal to the surface rather than being measured from the path to the surface itself.  The diagram below illustrates why angles are measured in this manner.

 The figures to the left illustrate a (red) light beam striking a surface that is not perfectly smooth. The angle between the beam and the surface will depend upon what point on the surface is used as a reference.  Measuring to a low point on the surface yields a measured angle of 48 degrees.  Measuring to a higher point on the surface yields the much smaller angle of 24 degrees. Measuring the angle between the beam and the normal to the surface always yields the same value of 37 degrees.

Determining the normal to a rough surface can be difficult, as the normal will have a different orientation at each point on the surface.  To construct a normal for such a surface, you must first draw a line tangent to the surface at the point where the light strikes the surface, then draw the normal which will be perpendicular to that tangent.  Although sometimes tricky, the task will yield a normal from which consistent measurements of angles can be made.

The angle of incidence is not the only angle so defined.  The reflected light will make an angle of reflection that is measured from the reflected beam to the normal, and light that is not reflected but continues into the second material will make an angle of refraction with respect to the normal.  These angles will be discussed later in this lesson.

 Can we predict which direction the light ray will travel after reflecting  from the surface? Go to the next page to find out!