Kaitlyn Greiner

Formal Lab Report: Interference of Light

Date Performed: July 30th, 2014

Lab Partners: Erin Phlegar and Stephen Few Physics 102 L, Section: 02

Professor Teklu

Abstract: We set out to study the interference patterns of light that passed through single and

double slit slides. This interference proves that light behaves like a wave. We calculated the wavelengths of red and green lasers shining through double and single slit slides. We observed the patterns they made after passing through the slits. We found constructive and destructive

interference in the patterns. This shows that the interaction, called interference, took place, which shows that light behaves like a wave.

Introduction: In this experiment, our goal was to study the interference patterns of light through a

single and double-slit using a laser of two different colors. From Thomas Young’s work, we know that light behaves like a wave because it forms interference patterns when shown through a double slit. Since we know that light behaves like a wave, we can measure the wavelengths of

colors of light. Light rays interact if more than one passes through the same place (slits) at the same time. This experiment will focus on the interference of light. After the light rays have

passed beyond the slit(s), the electric and magnetic fields oscillate and result in the sum of the waves. This is an interaction called interference. Interference can be constructive or destructive. Constructive interference means that two waves are in phase with each other and create a wave

with higher amplitude. This means that one wave has to be a whole number of wavelengths past the other wave so that they are in phase. This “path difference” can be calculated with the

formula, dsinΘ, in a double slit experiment. Destructive interference means that two waves are out of phase with each other and result in a cancellation of the two waves. In a single slit experiment, we will focus more heavily on this destructive interference.

We expect to find a bright central band during a single slit experiment. The band shows light that has passed without interference. We expect this pattern to be very spread out and for the bright

spots to quickly diminish from the bright center. We are expecting to see a finer pattern and that appears more uniformly bright in the double slit experiment.

Description of Apparatus:

We set up a laser (red or green) behind a single or double slit slide on a mount and placed a piece of paper further away after the slide. We taped our piece of paper on some boxes to stand

it up. Our patterns were projected here on this sheet of paper. We measured the distance, L, from our slit slide to our piece of paper. Sometimes, we had to change this distance in order to see our

pattern more clearly. To do this, we slid the laser and slide to various locations on the mount. We found our values for Y by measuring parts of the pattern projected on the sheet of paper. The parts that we measured for Y varied for the double slit and single slit experiments. We used these

values to calculate our angle, Θ, between the beam path and the pattern. In the double slit experiment, we were given our slit spacing, d, on the slide. In the single slit experiment, we were

given our width of the slit, a, on the slide. This description is depicted in the sketches below:

Procedure:

We set up a laser behind a single or double slit slide and then placed a piece of paper

after the slide. For the double slit experiment, we used a red laser and then a green laser and determined the wavelength of each color. We chose the distance, d, between the two slits on our double slit slide to be .5mm. After getting our red laser set up behind the double slit slide, we

measured the distance, L, from this slide to the paper on which the pattern was being projected. Next, we found Y by observing the pattern on our sheet of paper. We measured the length of our

entire central, bright pattern then counted the bright fringes within this pattern. We divided its length by the number of bright fringes counted. We calculated the angle between the beam path and the pattern by using the equation, tanΘ=Y/L. Since the zeroth order band is in the center of

the interference pattern, our value for m is one. After we found the angle, we were able to plug everything into the equation, mλ=dsinθB, and solve for the wavelength of the red laser. We

compared our result to the actual value of 650nm and calculated our percent error. We repeated this same process for the green laser. We kept our distance, d, between the

two slits the same but we changed our length, L, in order to see our pattern more clearly. Our

value for the order of the interference band, m, remained one. We calculated using the first order band throughout this experiment. We solved for the wavelength of the green laser and compared

our result to the actual value of 532nm. We calculated a percent error. For the single slit experiment, we used a red laser and a green laser and determined the

wavelength of each. We replaced our double slit slide with the single slit slide. We chose a

width, a, on our single slit slide to be .04mm. We measured the length, L, in the same way from the single slit slide to the piece of paper. We found Y measuring the distance from the middle of the dark space above our main pattern to the middle of the dark space below our main pattern

and dividing this value by two. We divided by two because the value of y1 is actually from the middle of our main pattern to the middle of the next dark space. By measuring from the middle

of a dark space to the next middle of a dark space, we were actually finding 2y1. We, then, calculated our angle using our Y and L. The value of the order of the interference band, m, is still one. We then plugged all of these values into the equation, mλ=asinθD, to calculate the

wavelengths for the red and green lasers. Again, we changed the length, L, slightly for the green laser in order to see the pattern more clearly. We compared the calculated wavelength value for

the red laser to 650 nm and calculated our percent error. We compared the calculated wavelength value for the green laser to 532nm and calculated our percent error.

Results:

Double Slit-

mλ=dsinθB

Red laser:

D=.5mm or .5x10^-3m L=166cm or 1.66m

Y=5.1cm/23 bright fringes

Y=.222 cm or .00222m tanΘ=.00222/1.66

Θ=.077

M=1

Mλ=dsinθB

(1)λ=(.5x10^-3)sin.077 λred=6.68x10^-7m or 667.9 nm

actual: 650 nm

% Error: ((650-667.9)/650)x100%

=2.75%

Green Laser:

D=.5mm or 5x10^-3m

L=205cm or 2.05m Y=5.1cm/24 bright fringes

Y=.2125cm or .002125m tanΘ= .002125/2.05

Θ=.059

M=1 (1)λ=(.5x10^-3)sin.059

λ=5.18x10^-7m or 518.3 nm

actual: 532 nm % Error:

((532-518.3)/532)x100% =2.58%

Single Slit-

mλ=asinθD

Red Laser: w=.04x10^-3m

L=127.2 cm or 1.272m

Middle of dark to middle of dark=4.5cm 4.5/2=2.25cm or .0225m Y=.0225m

tanΘ=.0225/1.272 Θ=1.01

(1)λ=(.04x10^-3)sin1.01 λ=7.07x10^-7m or 707.4 nm

actual: 650nm

% error: ((650-707.4)/650)x100%

=8.83%

Green Laser: w=.04mm or .04x10^-3m

L=140.5 cm or 1.405m

Middle of dark to middle of dark=4.1cm 4.1/2=2.05cm or .0205m Y=.0205m

tanΘ=.0205/1.405 Θ=.836

(1)λ=(.04x10^-3)sin.836

λ=5.84x10^-7m or 583.6 nm actual: 532nm

% Error:

((532-583.6)/532)x100% =9.70%

Data Table:

Double Slit (calculated)

Double Slit (% Error)

Single Slit (calculated)

Single Slit (% Error)

Red Laser 667.9 nm 2.75% 707.4 nm 8.83%

Green Laser 518.3 nm 2.58% 583.6 nm 9.70%

Conclusions:

This experiment proved the wave theory of light, that light behaves like a wave. We proved this by calculating the wavelengths of the two different colored lasers by observing their

patterns. After comparing our calculations to the actual values of the wavelengths, we found that we had very low percent errors. This shows that our formulas are very effective in finding wavelengths of light. Our patterns showed the interaction of the light waves. There was not a

large difference in the patterns between the different colors. We did find that double and single slits generate slightly different patterns of light. The double slit pattern has very distinct bright

and dark bands of light and does not fade at the ends. The single slit pattern has a bright central

pattern that is less distinct and blurrier. This pattern faded at the ends. Both patterns had dark and bright bands. Constructive interference creates a wave with higher amplitude and is shown in the

experiment as the bright bands of light in the patterns. This means that the waves arrived at the sheet of paper in phase with each other. The dark bands that appeared in this experiment show destructive interference, meaning the waves arrived at the sheet of paper out of phase with each

other. They cancelled each other out and no light resulted in these places. These observed interactions show that the interference of light took place.