In dealing with refraction of waves, it's important to distinguish between wave fronts and rays and understand how to use both.  The distinction is made at the beginning of section 26-5.  Figure 26-21 in the text shows a construction with both wave fronts and rays and also shows two ways to determine the angles of incidence and refraction.  The most common mistake in doing refraction problems is to use the complements of the angles.  Here, then, are two important things to remember:

• The angle of incidence (or refraction) is the angle between the the incident ray (or refracted ray) and the normal to the boundary between the media.

• The angle of incidence (or refraction) is the angle between the the incident wave front (or refracted wave front) and the boundary between the media.

We'll begin with a problem where the wave fronts are parallel to the boundary.  Both the angles of incidence and refraction are 0° in this case.  Refer to Figure 1.  How do the wave speeds in the media above and below the boundary compare?  The key to comparing them is to realize that the constant in this situation is the wave frequency.  Remember the problem with the two strings tied together and vibrated at one end with the saw motor?  That situation is analogous to this one.  In the case of the strings, the frequency was the same for both strings.  That led to the conclusion that wave speed was proportional to wavelength.  The same applies to the situation in Figure 1.  The wave speed is greater where the wavelength is greater.

Figure 1	Figure 2

Part A.

Submit your answers to this part in the corresponding electronic form.

1.  Open this applet now.  The situation is similar to the one depicted in Figure 1.  The problem is to determine the frequency, wavelength, and speed of the waves in the media below and above the boundary.  The width of each medium (bottom to top) is 10.0 cm. The grid is exposed on the right-hand side of the screen to aid in making measurements.

2.  Next consider Figure 2 above.  Assume the media are the same as those in the applet.  That means the wave speeds and wavelengths have the same ratio as in the applet.  However, the angle of incidence is no longer 0°.  You know from a derivation in 26-21 that v_rsinq_i = v_isinq_r.  (We're using the subscripts 'i' and 'r' for incident and reflected instead of the 1 and 2 that the book uses.)  What is the value of the ratio sinq_i/sinq_r?  Why will this value be the same as long as the media are the same?  Explain. Will the ratio be the same if we change the frequency of the incident waves?

3.  For the situation of Figure 2, assume that the angle of incidence is 30°.  Determine the angle of refraction to the nearest degree. Again, assume the same wave speeds as in the applet.

Part B.

Submit your answers to this part on paper.

The following problem requires a construction on paper.  Click here to open a template.  Print it now.  The template shows periodic plane waves passing over a straight boundary from one medium to another.  Do the following.  Use a ruler to draw straight lines and make measurements.

1. Call the point where wave front 1 intersects the boundary P, and construct the normal to the boundary at this point.  Extend the normal on either side of the boundary.

2. Construct the incident ray that intersects the boundary at point P.  Then label the angle of incidence as measured with respect to the normal.

3. What is the value of the angle of incidence?  You don't need a protractor for this.  Use trigonometry.

4. Where the incident waves touch the boundary, construct refracted wave fronts at an angle of 45° to the boundary.  Once again, you don't need a protractor.  Just draw lines with a slope of 1.

5. Construct the refracted ray that intersects the boundary at P.  Then label the angle of refraction as measured with respect to the normal.

6. Measure the wavelengths of both the incident and refracted waves.  Then use the wavelengths to calculate the ratio of the wave speeds v_r/v_i.

7. Using the angles of incidence and refraction, calculate the ratio of the wave speeds.

8. Compare your answers to steps 6 and 7.  Why should they be equal to within measurement error?