Activity 07: Diffraction Through a Circular Aperture

In today's activity, you will look at diffraction patterns from two different wavelengths of light.

Equipment needed: Each group needs an optics bench, a red laser with power cord, a slide with circular apertures, a variable diaphram slide, a screen, and two magnetic optics carriers. Groups will take turns with the green lasers with power cords..

Before You Start:
Answer the following questions to the best of your ability before doing the experiment.

You should be familiar with the equation sin q ~ y/D = 1.22 l/d. Identify each of the variables and what they represent.
The central maximum in a diffraction pattern determines the minimum bit size on a CD-ROM. How will the size of this maximum change if (a) A wider aperture is used? (b) The disk is located further from the opening? (c) A smaller wavelength of light is used?
Which do you think has the smaller wavelength: green or red? Which will produce the smaller diffraction pattern?

After you have thought about your answers, compare notes with your group members. Does everyone have the same predictions, or are there differing opinions?

LASERS ARE NOT TOYS. DO NOT LOOK INTO THE LASER OR POINT YOUR LASER WHERE IT SHINES IN SOMEONE'S EYES. WHEN YOU ARE NOT USING THE LASER, UNPLUG IT OR TURN IT OFF.

Set up the equipment on the optics bench as shown to the right. The optics bench should be oriented so you can see the ruler. The red laser should be down at the left end of the bench. Since the lasers tend to get jarred, take the time to align your laser so it shines down the middle of the optics bench.

The circular aperture slide should be placed on the left side of one optics carrier, and the white screen with ruler should be placed on the left side of the other optics carrier. Push both carriers flush against the side of the optics bench. We want to use the 0.08 mm aperture, which is the second from the left when looking at the slide so with the label up. Keeping the optics carrier flush against the side of the bench, move the slide on the carrier until the laser light shines through the appropriate aperture. Adjust the position of the screen until you can clearly see a central maximum and the next maximum ring. You will probably have 20-30 cm between the two optics carriers.

Diffraction Pattern of a Red Laser

1. Move the screen slowly away from the aperture slide. What variable does this change? What happens to the width of the central maximum (bright circle) as you move the screen away from the aperture?

2. Does this behavior match what you predicted from the diffraction equation? How or how not?

3. Without moving the optics carriers, shift the aperture slide to the 0.04 mm opening. What variable does this change? What happens to the width of the central maximum when you decrease the diameter of the aperture?

4. Does this behavior match what you predicted from the diffraction equation? How or how not?

If a green laser is available, skip to the next section (Q12 - Measuring the Wavelength of a Green Laser) and do it before returning to this section (Q5).

Measuring the Wavelength of a Red Laser

Adust the aperture slide so that the 0.08 mm aperture is again in use. Slide the carrier with the screen away so that the central maximum gets as big as possible while still seeing the next ring. You will probably have about 30 cm between the carriers when this is accomplished.

5. Write down the positions x_aperture and x_screen of the optics carriers as given by the ruler on the optical bench. Notice that the numbers on the ruler correspond to millimeters.

6. Find the distance D between the aperture and the screen.

7. Measure the width of the central maximum, using the ruler on the screen. Note that the small divisions are millimeters, with the numbered divisions representing centimeters. To get accurate results, you must measure the width between the center of the dark ring on one side to the center of the dark ring on the other side. You must also measure the width to 1/10 of a millimeter by estimating between marks on the scale.

8. Divide the width by 2 to get y, the distance between the center of the pattern and the first minimum.

9. Find tan q from y, and D, then find sin q. Show your work.

10. Find the wavelength of the red laser from sin q and the aperture width d=0.08 mm.

11. Given that visible light ranges in wavelength from 400-650 nm (a nanometer is 10^-9 meters), and that red light has longer wavelengths than other colors, is your result for the wavelength of the red laser reasonable? Why or why not?

Measuring the Wavelength of a Green Laser

LASERS ARE NOT TOYS. DO NOT LOOK INTO THE LASER OR POINT YOUR LASER WHERE IT SHINES IN SOMEONE'S EYES. WHEN YOU ARE NOT USING THE LASER, UNPLUG IT OR TURN IT OFF.
Replace the red laser with a green laser. The green laser comes with a cap over it. Remove this cap when you are using the laser, and replace it when the laser is not in use. It is particularly important to take care with the green laser since it can do damage to eyes.
Adjust the optics carriers and slides until you get a clear diffraction pattern on the screen. But do not drastically change the distance between the aperture and the screen.

12. Write down the positions x_aperture and x_screen of the optics carriers as given by the ruler on the optical bench. Notice that the numbers on the ruler correspond to millimeters.

13. Find the distance D between the aperture and the screen.

14. Measure the width of the central maximum, using the ruler on the screen. Note that the small divisions are millimeters, with the numbered divisions representing centimeters. To get accurate results, you must measure the width between the center of the dark ring on one side to the center of the dark ring on the other side. You must also measure the width to 1/10 of a millimeter by estimating between marks on the scale.

15. Divide the width by 2 to get y, the distance between the center of the pattern and the first minimum.

16. Find tan q from y, and D, then find q and sin q. Show your work.

17. Find the wavelength of the green laser from sin q and the aperture width d=0.08 mm.

18. Given that visible light ranges in wavelength from 400-650 nm (a nanometer is 10^-9 meters), and that green light has a wavelength near the middle of this range, is your result for the wavelength of the green laser reasonable? Why or why not?

Making Sense of It All

19. Which of your measured wavelengths, green or red, was smaller?

20. Which laser gave the smaller diffraction pattern, the red or the green?

21. Optical data is read by shining a laser beam on a CD-ROM. The lens used to focus the laser also acts as an aperture and diffracts the laser light. In order to resolve bits of data, no more than one bit may fall in the central maximum of the diffraction pattern. Which laser (red or green) will be able to resolve smaller bits of data? Why?

You will be asked to complete an evaluation of today's activity and lecture before the end of class. This evaluation counts as a free 5% of each activity grade. It will generally be done on WebCT in the last 5-10 minutes of class, but time constraints may lead to the occasional evaluation done on paper.

1.	Move the screen slowly away from the aperture slide. What variable does this change? What happens to the width of the central maximum (bright circle) as you move the screen away from the aperture?
2.	Does this behavior match what you predicted from the diffraction equation? How or how not?
3.	Without moving the optics carriers, shift the aperture slide to the 0.04 mm opening. What variable does this change? What happens to the width of the central maximum when you decrease the diameter of the aperture?
4.	Does this behavior match what you predicted from the diffraction equation? How or how not?

5.	Write down the positions x_aperture and x_screen of the optics carriers as given by the ruler on the optical bench. Notice that the numbers on the ruler correspond to millimeters.
6.	Find the distance D between the aperture and the screen.
7.	Measure the width of the central maximum, using the ruler on the screen. Note that the small divisions are millimeters, with the numbered divisions representing centimeters. To get accurate results, you must measure the width between the center of the dark ring on one side to the center of the dark ring on the other side. You must also measure the width to 1/10 of a millimeter by estimating between marks on the scale.
8.	Divide the width by 2 to get y, the distance between the center of the pattern and the first minimum.
9.	Find tan q from y, and D, then find sin q. Show your work.
10.	Find the wavelength of the red laser from sin q and the aperture width d=0.08 mm.
11.	Given that visible light ranges in wavelength from 400-650 nm (a nanometer is 10^-9 meters), and that red light has longer wavelengths than other colors, is your result for the wavelength of the red laser reasonable? Why or why not?

19.	Which of your measured wavelengths, green or red, was smaller?
20.	Which laser gave the smaller diffraction pattern, the red or the green?
21.	Optical data is read by shining a laser beam on a CD-ROM. The lens used to focus the laser also acts as an aperture and diffracts the laser light. In order to resolve bits of data, no more than one bit may fall in the central maximum of the diffraction pattern. Which laser (red or green) will be able to resolve smaller bits of data? Why?