Measurement of Slit Width

from the Diffraction of Laser Light

Preparation time

The time needed to assemble the materials is fifteen to twenty minutes.

Introduction

The diffraction pattern of light is the interference pattern created when light passes through a thin aperture or slit. This pattern depends on the number of slits or lines used in the diffraction plate. In this lab, the students use a diffraction plate with six different slits (A - F) to investigate the differences in diffraction patterns. (see diagram 1.) In the process, the students will make measurements to calculate the slit widths and center-to center widths .

SPECIAL SAFETY NOTE

Even though helium-neon lasers are not extremely hazardous, students should not look directly into the laser. Laser light is powerful because it is coherent (light of one wavelength) and the light waves are traveling in phase.

(see diagram 2)

Materials

(per lab group)

1 diffraction plate, 1 diffraction grating and 1 component holder.

(Pasco parts numbers:

Difraction plate 003-02742

Diffraction Grating 003-02756

Component Holder 648-02696)

a Helium-Neon LASER, which emits light at a wavelength of 640 nm

( a nanometer is 1 x 10 ^-9 m^, or one billionth of a meter)

white paper and a book, to construct a screen

meter stick and metric ruler

Procedure

Spend a few minutes reviewing the two diffraction patterns, math symbols and equations from the introductory worksheet . If the students did not complete the problems, work through some problems with the class.

1. Instruct the students to identify the variables in the equations on the first page of the lab. They need to know where to find the distances for the variables and how to make the necessary measurements on the paper screen Use the overheads, if needed, to help students during the lab. For a single slit grating the students measure y, L and calculate the value of w.

the equation states: _{[[lambda]] = yw [[lambda]] = 640 nm}

^L

For a double slit grating the students measure x, L and calculate the value of d

the equation states:

_{[[lambda]] = xd = d sin[[Theta]]} (Remember that [[Theta]] stands for the angle of incidence)

^L

2. Have the students set up the LASER and align the paper screen, then shine the light

through plates A - F. (they will complete a total of 18 measurements) All measurements

are made on the paper screed. Make sure they measure the values for L, y or x to within

+ 2 millimeters and record the data on page two. The alignment of the laser, diffraction

plate and screen must be the same for each measurement to guarantee consistent results.

Calculations, conclusions and final analysis

1. Using the equation , ^{[[lambda]] = yw Calculate the value of w for slit patterns A-C.}

^L

640 nm = yw w = 640 nm (L)

L y

(record answers on data table page 2)

2. Using the equation, ^{[[lambda]] = xd = d sin[[Theta]] Calculate the value of d for slit patterns D-F.}

^L

^{640 nm = xd d = 640 nm(L)}

^{L x}

(record answers on data table page 2)

3. Calculate the average value for w for slit patterns A-C and record in the data table, be

sure to include + notation. (+ for the final answer is a % of total calculated)

Pattern    Average value of w    
                  (mm)           
   A                             
   B                             
   C                             

4. Calculate the average d for slit patterns D, E and F. Put your answer in data table, be

sure to incluide +/- notation.

Pattern    Average value of d    
                  (mm)           
   D                             
   E                             
   F                             

5. Students will use the diffraction grating and duplicated the lab procedure. They need to

organize their own data table and interpret their findings. Since there are many

scratches (or slits), data collection and analysis will be a good challenge.

Conclusion

Describe in a paragraph or two, how LASER light can be used to determine the center-to-center distance for a two slit diffraction plate.

Students should be able to draw a diagram of the double slit plate, identify the location of x and L and show the calculations to determine the value for x.

Since [[lambda]] remains constant at 640 nm, and the calculations use the same equation

[[lambda]] = xd , students should be able to set up the experiment, explain data

L collection and analysis. They should also be clear and concise their explanation.