# Purpose

To determine the distance between two slits in a double-slit experiment. And, to determine the width of a slit in a single-slit experiment.

# Theory

The angular location of the maxima produced in a double slit experiment are given by the formula:

$d\sin \Theta = m \lambda$     (Eq. 1)

Here d is the distance between the slits, Θ is the angle measured from the central line, λ is the wavelength of the light used for the experiment, and m is any integer number, 0, ± 1,± 2, ….

Every slit has a finite width which affects the produced diffraction pattern regardless of the number of the slits. For a single slit, the only effect will be due to the width of the slit. The angular location of the minima produced by the a single slit with finite width is given by the formula:

$a \sin \Theta = m \lambda$    (Eq. 2)

Remember, a is the width of the slit, and even though the rest looks “similar” to that for the double slit interference pattern, the conditions are very different. The integer number m cannot have value of zero, since the central maximum is at that location: m = ± 1,± 2, ….

In the lab, it is difficult the measure the angle at which maxima or minima are produced in the interference/diffraction patterns. Because of that, you will project the pattern on a screen a distance L from the slits, and you will measure the actual distance, y, for the maxima (or minima in the case of single slit) as measured from the middle of the pattern.

Geometry will then give the angle:

$\tan \Theta = \frac{y}{L}$    (Eq. 3)

# Experimental Setup

CAUTION! You will be working with low-power lasers. To ensure safety, follow the lab safety rules:

• Position the lasers so that they point light towards the wall (and not the middle of the classroom, towards people)
• NEVER look directly at the laser.

Here is how the setup looks including the interference pattern.

# Activity 1. Double Slit Experiment

Set up the experiment with a double slit. Create an interference pattern on a screen that is at least 1.0 m away from the double slit.

Question: Do you know why you are told to keep the distance larger than 1.0 m?* (read the end for the answer!)

Place a paper on the screen and mark a portion of the interference pattern. Count the number of fringes (should be odd number for the central maximum and the left and right maxima). Determine y and m from the paper.  y will be half the distance between the farthest left and farthest right maximum. m is the order of the highest maximum you marked on the paper.  For example, if you count 17 fringes (maxima), then m = (17 – 1) /2 = 8. That is the order of the last bright fringe on your paper.

Using the distance y for the m-th order maximum, and the length to the screen, L, determine the angle at which that maximum appears (Eq. 3). Then, using Eq. 1, calculate the distance between the slits.

Compare your result with the distance published on the slide.

# Activity 2. Single Slit Experiment

Set up the experiment with a single slit. Create an interference pattern on a screen.

Attention! You will be marking the dark fringes (minima) in this activity.

Place a paper on the screen and mark a portion of the interference pattern. Count the number of DARK fringes (should be even number for the left and right minima). Remember, the center is maximum.

Determine y and m from the paper.  y will be half the distance between the farthest left and farthest right maximum. m is the order of the highest maximum you marked on the paper.  For example, if you count 6 dark fringes (minima), then m = 6/2 = 3.  That is the order of the last fringe on the paper.

Using the distance y for the m-th order minimum, and the length to the screen, L, determine the angle at which that minimum appears (Eq. 3). Then, using Eq. 2, calculate the width of the slit.

Compare your results with the value published for the single slit width.

***Answer the Question. If the distance from the double slit to the screen too small, there are two factors that can affect your results.

1. The closer the screen is to the double slit, the less your interference pattern