For this assignment, you'll use two figures from the envelope in your lab kit. See below for what the figures look like. Retrieve them now.

Figure 1	Figure 2

One of the topics that you studied in Chapter 14 was interference of sound waves. Review this assignment to remind yourself of the conclusions. Sections 28-1 and 2 of the text deal with interference as related to light waves. The concept of path difference as being a determinant of constructive or destructive interference applies to both sound and light waves and, in fact, to all periodic wave phenomena. These relationships are fundamental:  For two sources oscillating in phase, interference is constructive at a point if the path difference from the sources to the point is an integral multiple of a wavelength. The interference is destructive if the path difference is an odd multiple of half a wavelength.

The photo to the right shows an actual interference pattern for water waves. You're looking down on a shallow tank of water illuminated from below in order to provide strong contrast between crests (bright lines) and troughs (dark).  Two point sources bobbing in and out of the water in phase with each other at constant frequency (at the bottom of the photo) produce circular waves. The fuzzy gray lines radiating outward are lines of destructive interference. The water is relatively calm in these areas. The drawing that you'll use for this assignment is similar to the situation depicted in the photo.

Refer now to Figure 1 above. The construction represents parallel, plane wave fronts incident on a barrier with two small apertures labeled S₁ and S₂. The apertures act as sources of spherical wave fronts. Since any particular plane wave front reaches the sources at the same instant of time, the circular wave fronts oscillate in phase. Note that the solid lines represent crests of the waves, and the dashed lines represent troughs. Wherever solid lines or dashed lines intersect, there is constructive interference.  Wherever a solid line crosses a dashed line, there is destructive interference. Note also that the perpendicular distance between successive solid lines or between successive dashed lines is the wavelength. This is indicated in two places.

The points of constructive interference extending along the perpendicular bisector of the line segment joining S₁ and S₂ have been connected with a straight, solid line labeled A_o. Note that crests intersect with crests and troughs intersect with troughs along this line. The line is called a line of antinodes.  If the waves were sound, the loudest sound would be heard along this line. If the waves were light, the brightest light would be seen along the line. If the waves were water, waves of the greatest height or depth would be seen there. 

The dashed lines labeled N₁ are lines connecting nodes where crests intersect troughs. These are lines of complete destructive interference and are called nodal lines. There would be no sound, no light, or calm water along these lines. The subscript 1 indicates that anywhere along the N₁ lines, the difference in the distance that waves have to travel from the two sources is half a wavelength. There are two such lines symmetrically located about the A_o line.

The two A₁ lines are also lines of antinodes. Anywhere along these lines the path difference is 1 full wavelength.

Now you'll take measurements from the construction with the goal of determining the wavelength in 3 different ways. Use a soft lead pencil and bear down so that your work will show clearly when scanned. Measure distances to the nearest half millimeter (0.05 cm). Show calculations on a separate piece of paper.

1. Using a straightedge or ruler, draw and label the N₂ and A₂ lines. 

2. Method 1 of finding the wavelength is to measure it directly as the perpendicular distance between wave crests. Describe your measurement technique in order to make clear that you measured to the greatest accuracy possible. Provide all necessary data used in calculating the wavelength.

3. Method 2 is to measure the path difference and use the condition for constructive (or destructive interference). For one of the A₁ lines, draw a straight line from where A₁ crosses line L to the center of the S₁ aperture. Repeat for the S₂ aperture. Measure the lengths A₁S₁ and A₁S₂ and find their difference. Using the condition for constructive interference and the path difference, determine the wavelength.

4. Carry out Method 2 for one of the N₂ lines. You should, of course, expect to get a value for wavelength nearly the same as for the A₁ line.

5. Method 3 uses equation 28-1 in the text. Review that method (see Example 28-2) so that you can see what needs to be measured. Use the A₁ line again. Describe how you will determine the angle θ using a ruler only. Then take the measurements you need and calculate the wavelength.

6. Using the result of Method 1 as the accepted value, calculate the experimental errors for the three values obtained in steps 3-5.

7. For this step, use Figure 2. That drawing is similar to Figure 1, except that the wavelength is different. Use both Methods 1 and 3 to determine the wavelength. It's up to you to decide what lines you need to draw. Whatever you decide, clearly show and label the lines on the graph. Then show your calculations. Compare the two values of wavelength that you obtain.

Of the three methods that you used above, only one of them is practicable for measuring the wavelength of light. You can't use Method 1, because you can't see the wave fronts of light rays. Method 2 isn't practicable, because the path differences would be on the order of the wavelength of the light.  These differences are too small for you to measure with standard lab equipment. Method 3, on the other hand, requires distances that you can easily measure in the lab. It's the method that you'll use in the next lab to measure the wavelength of laser light.  

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