CU Boulder Equations of Diffraction Theory Wave Nature of Light Lab 8 Report Attached is a document with a lab focused on describing diffraction of light and use the equations of diffraction theory to predict diffraction patterns. There is no textbook provided, just the link listed below. This is the link needed to complete the lab: https://phet.colorado.edu/sims/html/wave-interference/latest/wave-interference_en.html Lab 08 – Wave Nature of Light

NAME:_______________

Time spent on Lab 08 = approximately 2 hours, does not need to be done at one sitting

Materials needed = Access to computer and high speed internet, Java installed on the

computer

Learning Objectives:

● Describe diffraction of light and use the equations of diffraction theory to predict

diffraction patterns

First proceed to the following website to complete the lab:

https://phet.colorado.edu/sims/html/wave-interference/latest/wave-interference_en.html

Once the page is open, you should see something like the screenshot below:

Figure #1

Before we begin experimenting with light, take a few minutes to watch this video:

And keep the simulator on the first tab to experiment with creating water waves!

The photograph below shows the interference of two water waves produced by two coherent

sources operating at the same frequency and in phase. The waves travel outward at a constant

speed from the two sources at the center bottom of the picture.

Figure #2

1.

Describe the pattern produced by the interfering waves.

Now in the simulator, select the laser as the wave source by clicking the icon which looks like

this:

.

Once you turn on your green laser, it should look like this:

Figure #3

This is a top down view depicting the peaks of circular light waves as green rings and the

troughs of these circular waves as the black rings.

2. Measure the wavelength of the light wave being produced. You will want to use the

simulator’s measuring tape.

Turn on the second light source by selecting the “interference” tab on the bottom of the

simulator and again switch to the laser mode. Once you have done this, the simulator should

look like this:

3. Explore the effect of changing the separation between the two sources on the interference

pattern. Describe your observations.

Now set the source separation to be 3.5 * the wavelength you measured in #2.

4. Locate two positions of maximum field movement above the central point. Using the

simulation’s tape measure, precisely measure the distance from each source to each

maximum as shown in figure #2. Organize your data in the table below. You may want to

expand the simulator size for ease of measuring, and “show the screen” to better view

where maximums occur.

Measurement #

L1

L2

L2- L1

(L2- L1)/

1

2

3

5. Calculate the difference in the distance of each source to each maximum and then divide

by the wavelength and record your answers in the last column of the table above.

6. What relationship between the differences and the wavelength best describes your data?

Why?

a. L2 – L1 = n* , where n = 0, 1, 2, 3,…

b. L2 – L1 = (n+0.5)* , where n = 0, 1, 2,3, …

7. Now locate two positions of minimum field movement above the center. Measure the

distance from each source to each maximum. Organize your data in a table.

Measurement #

L1

L2

L2- L1

(L2- L1)/

1

2

8. Calculate the difference in the distance of each source to each minimum and then divide

by the wavelength and record your answers in the last column of the table above.

9. What relationship between the differences and the wavelength best describes your data?

Why?

a. L2 – L1 = n* , where n = 0, 1, 2, 3,…

b. L2 – L1 = (n+0.5)* , where n = 0, 1, 2,3, …

The two-slit experiment is a method of producing two sources of coherent light waves, which

can interfere with each other. A source of monochromatic light of wavelength is incident on

two slits separated by a distance d. A screen is placed a distance L away. A diagram below

illustrates this experimental setup.

Figure #4

10. Imagine plane waves (light waves from a distant source or from a laser) hitting the two

slits on the left. Why might you consider the waves emerging from the slits to be from two

coherent sources of light waves?

11. We want to predict the positions P that will give us either a dark spot or a bright spot. Let’s

step through the argument for predicting a maximum. In the picture below, identify only the path

length difference between the light reaching P from the two slits. Indicate it with the Greek letter

.

Figure #5

12. If the point P is a maximum then what must the path length difference, , be in terms of the

wavelength? (Recall your work in the data tables above)

Figure #6

13. Now express in terms of d and sin θ.

14. Combine your expressions in 12 and 13, and write the resulting equation in the space

below.

15. Now, using the small angle approximation, ≈ ≈ , for angles less than about 20°,

solve for y (the position on the screen) in terms of , L and d.

16. What is the equation that gives the positions of the minimums along the screen?

17. If you increase d, the distance between the slits, what should happen to the bright spots on

the screen?

In summary, waves can interfere with one another and produce constructive and destructive

interference fringes. And when light waves pass through slits that are small compared to the

wavelength of the light, the waves can spread out and actually bend around corners! In this case

it does not produce a nice shadow of the slit as you might expect but behaves more like sound

waves bending around a doorway (where the width of the doorway is comparable to the

wavelength of the sound wave). Any time light waves encounter a very sharp edge or a very

small opening a diffraction pattern can develop like the one seen above. If there is time, have

your instructor show you the diffraction pattern from a CD or a diffraction grating.

●

Portions of this lab were taken from ©Humanized Physics Project (HPP), Doane

University.

Once you have completed all lab questions, please download this document as a PDF

only! Then upload this PDF to Blackboard under the assignment “Lab 08”, for grading.

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