Wave Interference
https://phet.colorado.edu/sims/html/wave-interference/latest/wave-interference_en.html
In your lab report, be sure to show calculations. And include screenshots.
Part 1. Double Slit Interference
In the pictures on the last page, the rays are
emitted in all directions from the slits, but
let’s concentrate on the rays that are
emitted in a direction toward a distant
screen ( measured from the normal to the
barrier). One of these rays has further to
travel to reach the screen, and the path
difference is given by
d sin .
Small angle simplification: If is small (<< 1
rad), then
sin (in radians),
and
bright spots occur on the screen at
d
m
=
; dark spots occur at
( )
d
m
2
1 = + .
As shown below, the angle (measured from the center of the screen) is related to the distance x
measured on the screen by tan()=x/L, where L is the distance from the screen to the source of light (the
aperture).
laser
aperture
screen
L
tan= x/L
x
If the angle is small (less than a few degrees), then to an excellent approximation, sin() tan() (in
radians) so the locations of the interference bright spots are given by
d
m
L
x
= = .
Procedures:
A) Set the slit width to 500 nm and slit separation to 1500 nm. Record your slit separation d in Table
1. B) Press the green button on the light generator and generate an interference pattern on the
screen. (Again, you should see something like what you see at the top of this page.)
C) Pull the measuring tape tool out of the box in the upper right and use it to measure L (using 3500
nm to 4000 nm), the distance between the slits and the screen. Then measure x the distance
from the center of the central bright spot to the center of one of the 1st order bright spots.
Record these values in Table 1. (Be sure to include units!!!)
D) Calculate the wavelength of the light λ using the diffraction formula derived in the Background
section. Record this value in Table 1.
E) Pause the simulation and use the measuring tape tool to measure the wavelength directly.
Record this value in Table 1.
F) Calculate the %-error between your calculated and measured values, and record this value in
Table 1.
G) Adjust the frequency of light and repeat steps B-F.
Color of
Light
Slit
Separation d
Distance
from
Slits to
Screen L
Distance
from
Central to
1
st
Order
Bright
Spot x
Wavelength λ
(calculated)
Wavelength λ
(measured)
%-Error
Red
Violet
Analysis:
1.What happened to the spacing of the bright spots when you increased the wavelength of the light?
2.Explain why your answer to #1 occurred.
3.What happens to the interference pattern if d is increased? What if d is decreased?
4. Explain your reasoning for 3. Insert screenshots here to prove your point.
5. Name one of the Applications. List the source of information.Part 2. Single Slit Diffraction
If the viewing screen is far away, the rays heading for any point on the screen are essentially parallel.
Consider the waves emanating from the upper half and lower half of the slit. Destructive interference, a
dark fringe, occurs if the path difference from any point in the upper half of slit and the corresponding
points in the lower half of the slit is an integer multiple of λ/2 so that the total electric field is zero. The
angle at which this occurs can be seen from the diagram to be
D sin θ=λ [first minimum]
The intensity is a maximum at θ= 0 and decreases to zero at the angle given by equation (3).
At a larger angle there will be a bright line, but not nearly as bright as the central spot at θ=0. As the path
difference becomes an integer multiple of λ/2, there will again be a minimum of zero intensity when
D sin θm=mλ
Procedures:
A) Set the slit width to 1600 nm.
B) Press the green button on the light generator and generate an interference pattern on the
screen.)
C) Pull the measuring tape tool out of the box in the upper right and use it to measure L (using 3500
nm to 4000 nm), the distance between the slits and the screen. Then measure x the distance
from the center of the central bright spot to the 1
st dark spots. Record these values in Table
1. (Be sure to include units!!!)
D) Calculate the wavelength of the light λ using the diffraction formula derived in the Background
section. Record this value in Table 1.
E) Pause the simulation and use the measuring tape tool to measure the wavelength directly.
Record this value in Table 1.
F) Calculate the %-error between your calculated and measured values, and record this value in
Table 1. G) Adjust the frequency of light and repeat steps B-F.
Color of
Light
Slit
width D
Distance
from
Slits to
Screen L
Distance
from
Central to
1
st
Dark
Spot x
Wavelength λ
(calculated)
Wavelength λ
(measured)
%-Error
Red
Violet
Analysis:
1.What happened to the patterns when you increased the wavelength of the light?
2.Explain why your answer to #1 occurred.
3.What happens to the diffraction pattern if d is increased? What if d is decreased?
4. Explain your reasoning for 3. Insert screenshots here to prove your point.
5. Name one of effects of diffraction seen in every day of life
