Interference, Diffraction, and Polarization         Name:_______________________

Partner(s):__________________________________________________________

Instructor Notes: Attach the linear translator to the optics bench close to the 0-cm end and set the aperture bracket to 1.

A. Double-Slit Interference

Purpose: To observe double-slit interference pattern and measure the wavelength of light.

Apparatus: Light sensor w/aperture bracket & cable, diode laser w/power adapter, multiple-slit set, optics bench w/linear translator, meter stick, rotary motion sensor, 750-interface, and PC.

Theory:

Bright fringes of a double-slit are given by (d is double-slit separation and λ is wavelength),

First bright fringe is given by, 

; (Y is fringe-width),    

Procedure:

1. Place the optics bench w/linear translator on the laboratory table.

2. Remove the rack from the linear translator by unscrewing the two rack thumbscrews.

3. Insert the rack through the slot in the side of the rotary motion sensor, step-pulley is facing up and the rod-clamp is facing the bench. Put the rack back and tighten it with rack thumbscrews.    

 4. Attach the light sensor with aperture bracket to the rotary motion sensor as shown below.

5. Mount the diode laser on the other end, at the 100-cm mark of the optics bench.   

6. Set the multiple slit to a double slit separation, d of 0.25 mm and place the double-slit at the 90-cm mark.  

7. Plug in the power adapter for the laser.

8. Adjust the position of the light sensor so that the laser beam strikes in the middle of the aperture bracket-1.

9. Move the rotary motion sensor/light sensor so that the interference pattern is away from aperture bracket-1.

10. Connect the rotary motion sensor to digital channels 1 (black) and 2 (yellow).

11. Set the gain to 100 in the light sensor and connect it to analog channel A.

12. Open DataStudio, click Open Activity, click Library, click Physics Labs, and click P35 Diffraction.

13. Open the Light Intensity versus Position graph display.

14. Click Start, and slowly and smoothly move the rotary/light sensor so that the whole interference pattern passes through aperture-1 of the light sensor.

15. Stop recording data and maximize the graph display.

16. Show the graph to the instructor.

17. Under the Data display double-click the 4^th title, Light Intensity VS. Position and open the Data Properties window and change the precision to 5.

18. Measure the total width for multiple fringes using the smart tool, double-slit to screen distance (L) with a meter stick, and complete the data table.

19. Print a hardcopy of the interference pattern and Close DataStudio, without saving. 

B. Single-Slit Diffraction

Purpose: To observe single-slit diffraction pattern and measure the wavelength of light.

Apparatus: Light sensor with aperture bracket, diode laser, single-slit set, optics bench, rotary motion sensor, linear translator, meter stick, 750-interface, and PC.

Theory:

Dark fringes for the single-slit diffraction are given by (w is the single-slit width and λ is wavelength),

For the first dark fringe (y is the half-width of the central dark fringe),

Procedure:

1. Remove the double-slit and replace it with a single-slit set to slit-width, w = 0.16 mm.

2.  Open DataStudio, click Open Activity, click Library, click Physics Labs, and click P35 Diffraction.

3. Open the Light Intensity VS. Position graph display.

4. Click Start, and slowly and smoothly move the rotary/light sensor so that the whole diffraction pattern passes through the sensor.

5. Stop recording data, maximize the graph display, and show the graph to the instructor.

6. Under the Data display double-click the 4^th title, Light Intensity VS. Position and open the Data Properties window and change the precision to 5.

7. Measure the width of the central bright fringe using the Smart Tool, single-slit to screen distance (L) with a meter stick, and complete the data table.

8. Print a hardcopy of the diffraction pattern and Close DataStudio, without saving.

DATA

A. Double-Slit Interference

# of fringes = N = _________

Width for the above # of fringes = _________________________________

Fringe-width = Y = __________

Double-Slit separation = d = _________

Double-Slit to Screen distance = L = __________

Wavelength (measured) = λ = dY/L = __________

Wavelength (accepted) = λ = ___________

                            % Error = ____________

B. Single-Slit Diffraction

Width for the central bright fringe = 2Y =  _______________________________

Half-width for the central dark fringe = Y = ________

Single-Slit width = w = _________

Single-Slit to Screen distance = L = __________

Wavelength (measured) = λ = wY/L = __________

Wavelength (accepted) = λ = ___________

                            % Error = ____________

C. Polarization

Purpose: Verify Malus’ law of polarization.

Apparatus: Optics Bench, Diode laser, power adapter for diode laser, Light Sensor with aperture bracket, Rotary Motion Sensor, Allen wrench (7/64”), Polarization kit with mounting bracket and belt, and Accessory Holder w/2 Brass Screws.

Theory: Once polarized light has been produced with a piece of polarizing material or with a laser, it is possible to use a second polarizer to change the polarization direction and simultaneously adjust the intensity of the light as shown in Figure 24.21 of your textbook. As in this picture the first piece of polarizing material is called the polarizer, and the second piece is referred to as the analyzer. The transmission axis of the analyzer is oriented at an angle q relative to the transmission axis of the polarizer. If the electric field strength of the polarized light incident on the analyzer is E, the field strength passing through is the component parallel to the transmission axis, or E cos q. According to Equation 24.5b, the intensity is proportional to the square of the electric field strength. Consequently, the average intensity of polarized light passing through the analyzer is proportional to cos²q. Thus, both the polarization direction and the intensity of the light can be adjusted by rotating the transmission axis of the analyzer relative to that of the polarizer. The average intensity of the light leaving the analyzer, then, is

(24.7)

where is the average intensity of the light entering the analyzer. Equation 24.7 is sometimes called Malus’ law, for it was discovered by the French engineer Etienne-Louis Malus (1775–1812).

Figure 24.21 Two sheets of polarizing material, called the polarizer and the analyzer, may be used to adjust the polarization direction and intensity of the light reaching the photocell. This can be done by changing the angle q between the transmission axes of the polarizer and analyzer.

Procedure:

1. Remove the light sensor with aperture bracket from the rotary motion sensor, which is attached to the linear translator.
2. Remove the rotary motion sensor from the linear translator.
3. Remove the rod clamp from the rotary motion sensor by removing the two silver screws on the clamp with the use of an Allen Wrench as shown below.

4. Attach the rotary motion sensor to the polarization kit as follows:
1. Remove the plastic belt and two thumbscrews from the polarization kit.
2. Line up the holes from mounting bracket with the holes of the rotary motion sensor and attach the two thumbscrews as shown below. (Make sure that the three-step pulley is facing in and the silver rod is pointing out.)

c. Place the plastic belt around the three-step outer-pulley on the Rotary Motion Device and the groove on the polarizer as shown above.

5. Attach the light sensor with the aperture bracket to the accessory holder as follows:

1. Remove the brass screws from the accessory holder.
2. Line up the screw holes of the accessory holder with that of the Light Sensor.
3. Using the 2 brass screws, attach the Light Sensor to the accessory holder.
4. Set the light sensor gain to 1 and aperture disk to #6.

6. Positioning of the apparatus:
1. Place the newly assembled Light Sensor with aperture bracket at 50 cm.
2. Place the Polarization Stand at 30 cm.
3. Place the Diode Laser at 100 cm, and turn it on.

7. Connect the cable from the Light sensor to port A, and the Rotary Motion Sensor to ports 1 (yellow) and port 2 (black).

8. Open Data Studio, click Create Experiment, select light sensor, select digits display, and select %Intensity.

9. Click “Start” and rotate the polarizer until the %intensity is a maximum. Record the maximum %intensity transmitted.

________________________________

10. Open activity P34 Malus’ Law.
11. Double Click on the graph display “%Intensity VS. Angular position.
12. Click Start and rotate the polarizer through one full turn.

13. Show the graph display to the instructor and if it is O.K print a hard copy.

14. Describe below how your results verify Malus’ law of polarization.