Learning object #9 for Physics 101 class.

1. Double Slit
Experiment

2. What is the Double Slit
Experiment?
 It shows the effects of interference in light waves
 Summary:
 Two light rays pass through two slits
 They are separated by a distance “d” striking a screen a
distance “L” from the slits
 If the d<<L then the difference in path length traveled by
the two waves is dsin0

3. This Learning Object
The purpose of this learning object is to show a
comprehensive mathematical example on double slit
experiments. It links different equations together to show
their relationship with one another.

4. An example:
 A laser beam with wavelength of 532 nm illuminates a
double slit and produces an interference pattern on a
screen a certain distance away. The distance between the
m=0 fringe and one of the m=1 fringes is 0.700 cm on
the screen. When q is equal to 90 degrees, m is equal to
11.2. Given this information, how far away is the screen?
*This question is derived from example 28-1 in the textbook, however it requires a different
approach and is asking you to solve for different values.

5. Solution:
We know the following values:
l= 532 nm
y= 0.700 cm for m = 1
m = 11.2 for q= 90 degrees
*** We want to know the value of D.

6. The equations:
 The following equations will be useful in obtaining our
answers:
1. tan q = y/D we want to find D, but theta value is also unknown.
2. d = ml/sin q  we can find theta first, but we don’t know d.
3. m = dsinq/l  we can find d here, all other values are known.

7. Solution
We start by using equation 3:
m = dsinq/l
We know the maximum value of m is found when q is equal
to 90 degrees. Therefore the only unknown value in this
equation is d.
d = ml/sinq
= (11.2)(5.32 x 10-7 m)/sin(900) = 5.96 x 10-6 m

8. Solution:
Next we use equation 2:
d = ml/sin q
We now know the value of d, so we can manipulate the
equation to solve for q. These values all pertain to m=1.
sin q = ml/d  q = sin-1(ml/d)
q = sin-1(1 x 5.32 x 10-7m/5.96 x 10-6 m)
q = 5.120

9. Solution
Finally we can make use of our first equation to solve for D:
tan q = y/D
We now know the value of q to be 5.120, and from the question that
y = 0.700 cm.
D= y/tan 0
D= 7.0 x 10-3 m/ tan (5.410) = 7.81 x 10-2 m
So therefore the interference patter produced by the laser beam
is on a screen 7.81 cm away!