Travis Henderson

Light Diffraction

BPHYS 123

Summer 2015

Diffraction Proves Light Is Wave-like, and Not Just a Stream of Particles

The general consensus of the modern science world is that light's properties are more wave-like rather than that of just a steady stream of particles. That is to say light behaves like the ripples of water when displaced by a pebble, rather than just water flowing from a hose (Michael W. Davidson, FSU). To further explain this analogy when a wave of water reaches a barrier it will propagate through the opening of it like so:

While my drawing doesn't reflect it, the frequency of the wave does not change when going through diffraction (how many times a wave repeats itself in a second, that is how many times it goes up and down):

The wavelength does not change as well (the distance it takes for a wave to repeat itself):

*http://www.studyphysics.ca/newnotes/20/unit03_mechanicalwaves/chp141516_waves/images/wavelength.png

Such is how water will behave through going through a barrier with an opening, light will also behave the same way going through a slit. However, once multiple slits are added to the barrier something interesting happens. While the wave will propagate outward just like in the single slit example, the waves coming from the two different sources travel different distances which creates interference. Interference is when you have more than one wave interacting with each other. With multiple slits for the light to pass through, what is essentially made is multiple sources for the light to propagate through. With diffraction, it is observed that some of the light interferes constructively and destructively. What this means is that the waves are just additive:

when troughs line up with troughs and crests line up with crests (this is called "in-phase"), the wave goes up and down by a greater magnitude producing a brighter light, whereas if a trough lines up with a crest the sum is zero (this is called "out-of-phase") which would make no light. This holds the same if the waves are only slightly out-of-phase. If these ideas of how light behaves like waves are true, then one should be able to calculate the wavelength of a red laser through multislit diffraction which is exactly what my lab group set out to do. We also thought we would be able to determine the width of a single slit using diffraction as well.

What my group did was pass a red laser through a diffraction grating (a plate with many, many slits) and projected this onto a screen with a scale on it. The lab set up was as such:

When the laser passed through the diffraction grating it projected onto the scale like, so:

*Florida State University http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/

there's different intensities of brighntess (or no brightness at all) of the laser projected onto the scale. This is due to what was stated before about interference. When the laser leaves the grating, some of the waves have to travel a farther distance to reach the same place on the scale than other waves that leave the grating. This can be illustrated with this diagram:

The wave labeled 2 has to travel a distance 1 further, than wave 1. Then wave 3 has to travel distance 2 further than wave 1. These different distances create the interference pattern displayed in the previous figure. The measurements my group took were that of the distance between the zeroth maximum (the brightest spot that's right in the middle, this distance called D) to the first maximums on each side individually (y1 and y2).

With the measurements we took we were able to find the angle using:

tan =Y/d

Captial Y being the average of y1 and y2. The significance of finding this angle was then used to find the wavelength using the following equation:

n*=d*sin

Where n = the order of the maximu from the central, in our case it was one since we were using the first maxima for the experiment. is the wavelength which we solved algebraically for, d is the grating element (lines/mm), and for theta we used the angle we found in the previous equation. With this lab setup, my group found the wavelength of the red laser to be 663 nm which is really close to the 650 nm listed for the lasers specs.

Because of what we measured for the wavelength based on the ideas that light would behave in a wave-like manner proves that in fact that light is wave-like, otherwise these results would not have been possible. To expand on the equation n*=d*sin :

*DESC Science http://www.showme.com/sh/?h=St4bFIm

When the light passes through the grating it is seen that it propagates at different spots depending on what slits it comes from, and thus travels different distances to reach the same spots. It can be observed that these wave paths make right triangles:

*DESC Science http://www.showme.com/sh/?h=St4bFIm

hence this is where the equation (n*=d*sin ) is derived from.

While calculating the waveform for the laser went just as expected, we also tried finding the width of single slits of unknown width. This did not go over well. Using the same concepts to find wavelenth we tred to find the width using the equation:

Y1= *L/a

where

= wavelength of the laser

Y1 = is the distance between the zeroth maximum and the center of the 1st minimum

L = distance from the zeroth maximum and the diffraction plate window

a = width of the slit.

We're able to use this equation because for small angles:

tan =sin

=a sin =atan

=ayL

a=L/y

Unfortunately, our reults had an error of 43%-74% depending on what slit we measured where the greater error was with greater widths of a slit.

While our second experiment didn't go as planned, I still believe that one can draw that conclusion that light does have wave-like properties. Even though our measurements for single slit diffraction were incorrect, we still wouldn't have been able to take the measurements we did had light not behaved like waves. To get better results for this taking more precise measurements would have been better, as well as doing the experiment in a more ideal environment with much less lighting. Also, taking more measurements of higher order maximas rather than just the first would probably also be beneficial since just having more data in general can give much more solid evidence.

Changes Made

I don't think I really addressed everything that was listed in the rubric. I really only used three sources for writing the content of this paper: the FSU and showme link, and then the textbook used in class. And of course, what was lectured in class. I only cited the FSU source directly in the text because the comparison they made with light waves being like water from a garden hose is their idea. Otherwise the whole idea of diffraction I felt was difficult to cite in the text because it's not really anyone's unique idea, what I wrote is a culmination of those sources.

I also tried to do a better job of labeling the pictures and diagrams in my paper. And as far as the scientific question being too broad, I'm acknowledging it is and I've done nothing about it. I hope that doesn't come across as having an attitude or anything like that, it's just that was kind of the best question I could come up with for that lab experiment since all my group wanted to do was just find the wavelength of a laser and the width of some slits using diffraction. I supposed maybe those could've been my scientific question? I just felt it was harder to write a more effective paper just relating to those two instances of diffraction, it just seemed more right to answer a more encompassing concept.

Enjoy the rest of your summer, Dr. Gliboff!

work cited:

http://www.studyphysics.ca/newnotes/20/unit03_mechanicalwaves/chp141516_waves/images/wavelength.png

http://www.reachoutmichigan.org/funexperiments/agesubject/lessons/bubbles.html

http://www.showme.com/sh/?h=St4bFIm

http://micro.magnet.fsu.edu/primer/lightandcolor/particleorwave.html

http://micro.magnet.fsu.edu/primer/java/interference/doubleslit/

Physics for Scientists and Engineers by WH Freeman