Science
Grantham University Week 1 Diffraction and Interference of Light Lab Report

Physics II

Grantham University

Question Description

PH221 – Week 5 Lab

Interference and Diffraction

Welcome to the Lab component of Physics II. All our labs use simulation applications of real laboratory equipment that are combined with measurement and graphing tools to allow you to explore, observe and analyze experiments. Each week you will complete one laboratory exercise using a virtual lab application and then use your results to write a formal lab report. Each experiment will be based around one main topic.

For this week’s lab you will use the Interference and Diffraction simulation. Download and read the following user guide to familiarize yourself with the simulation.

Download the instructions for two laboratory activities you will complete this week. You may wish to print them out and use to collect and organize your results.

Interference and Diffraction Lab

Use the answers to the laboratory questions to help you write your lab report. Your report will focus on Parts I and II of the lab. You should discuss the results obtained in the single vs. double slit experiments.

The lab report will have the following six sections. Include section headings in bold at the beginning of each section.

1.Introduction – Explain the purpose of this laboratory and what results you expect to see in this experiment.

2.Background – Discuss the concepts that form the foundation for this lab. You should address what you learned from the weekly lectures and readings that are related to the lab.

3.Methodology – Describe the apparatus that was used in the experiment(s) and how it was used in performing the experiments. Also explain what tools were available within the laboratory that allowed you to collect or analyze the data.

4.Data – Enter the data that you collected in the lab. You can use screen shots from the Data Table within the Pivot Interactives labs. Data should be clearly labeled with physical quantities and units.

5.Analysis – Analyze your results. If your Data Table included Calculated Columns, then the equation you used in those calculations should be included and described here. Any graphs created with the data go in this section, as well as your interpretations of their meaning. Were your results consistent with your original expectations?

6.Conclusion – Provide a concise summary of the results of your experiment(s) – what you did, what you found and what it means. Speculate on possible sources of experimental error and/or uncertainty within the experiment. Describe an additional experiment that could be run with this equipment to expand on what you’ve learned OR explain how you could use this equipment to answer another real-world problem.

.

PH221: Rubric for Laboratory Assignment 5

OVERRIDE GRADE OF 1:

If a PDF file is used, name and GID must be on each page.

All of most of the screenshots are missing.

Screenshots lack a time stamp (when indicated)

Lab worksheet file(s) not submitted along with the lab report.

The following screenshots required with a computer timestamp included:

- Screenshot of Double Slit experiment (Part I)

- Screenshot of Single Slit experiment (Part II)

Lab Report

The lab report should focus only on the experiments found on Parts I and II of Interference and Diffraction of Light Lab.

Introduction

10

The purpose of the lab is clearly stated and is aligned with the lab objectives. Expected results are proposed.

8

The purpose of the lab and expected results are stated and consistent with the assignment.

6

The purpose of the lab and expected results are stated but lacks clarity or is not consistent with the assignment.

2

The stated purpose is not aligned with the lab objectives or missing key elements.

0

The introduction is missing.

Background

10

The concepts that form the foundation of the lab are discussed. Reference to the weekly lectures or readings are made.

8

Concepts that underly the lab are discussed, but no reference is made to the weekly lectures or readings.

6

Concepts that relate to the lab are discussed but are vague or contain minor errors.

2

Underlying concepts are described but reveal major errors in understanding.

0

The background was not addressed

Methodology

-Include a screenshot of the interference and diffraction apparatus and description of how it works.

10

Methods, materials and equipment are specifically described using proper terminology. Concise, but detailed, procedure is provided.

8

Methods, materials and equipment are described, and a detailed procedure provided, but minor errors in terminology or descriptions are made.

6

Materials, methods and equipment are described, and a procedure provided, but they are too brief or vague to easily follow.

2

Some materials, methods and procedures are described, but they are not coherent or missing major pieces.

0

The methodology was not provided.

Data

Include:

- Screenshot of Double Slit experiment (Part I)

- Screenshot of Single Slit experiment (Part II)

20

Adequate data is collected in the lab is presented in a logical way that is organized and clear. Data is relevant to the purpose of the lab. Tables and observations are complete, clearly labeled, and physical quantities and units are given when appropriate.

15

Adequate data is provided and relevant to the purpose of the lab, but with minor errors in labeling or units. Tables and observations are complete and generally include captions and units.

10

Relevant data is provided, but it is not adequate to address the purpose of the lab or contain errors or omissions so that it is difficult to derive useful information from the data.

5

Data provided is not relevant to the purpose of the lab. Data is not organized or major errors in labeling and units appear throughout.

0

Little to no organization of the data was present. Lacks data.

Analysis

Include:

- Table 1 – Double Slit Diffraction with calculated values included

- Table 2 – Single Slit Diffraction with calculated values included

20

Data is analyzed appropriately, and key results are presented in a logical sequence. All required calculations are included. Sample calculation(s) are provided to show how the calculations were done. All variables include units when appropriate.

15

Data is analyzed, but with some details missing. All required calculations are included but with minor errors.

10

Data is analyzed, but with key details missing or inaccurate. One of the required calculations is missing or major mistakes made in the calculations.

5

Data analysis is included but does not include the required calculations or major errors in the calculations are made.

0

Date analysis is lacking.

Conclusion

30

Conclusion contains a concise summary of the results, speculates on the possible sources of error and uncertainty in the lab, and proposes an experimental extension of the lab or applies its concepts to a real-world situation.

20

Conclusion is provided, but only two of three elements are well addressed.

10

Conclusion is provided but only summarizes the results.

5

A conclusion is provided, but does not communicate useful information about the results, sources of error or possible laboratory extensions.

0

A conclusion was not provided

Unformatted Attachment Preview

KET Virtual Physics Labs KET © 2019 Name School ____________________________________ Date Lab 27.1 – Interference and Diffraction of Light Lab “No one has ever been able to define the difference between interference and diffraction satisfactorily. It is just a question of usage, and there is no specific, important physical difference between them. The best we can do, roughly speaking, is to say that when there are only a few sources, say two, interfering, then the result is usually called interference, but if there is a large number of them, it seems that the word diffraction is more often used.” – Richard Feynman’s Lectures on Physics, Vol. 1 Purpose • To observe the behavior of light passing through various configurations of slits. • To investigate how the width of a slit and the wavelength of the light passing through it determine the diffraction of light. • To determine the wavelength of laser light from the diffraction pattern produced when it passes through a single slit. • To determine the wavelength of laser light from the interference pattern produced when it passes through a pair of slits. • To measure the width of a narrow slit from the diffraction pattern produced when laser light passes through it. • To investigate the role played by single slit diffraction in the variation in intensity of a double slit interference pattern. Equipment Interference and Diffraction Apparatus PENCIL Figure 1: Interference and Diffraction Apparatus VPL_Lab - Interference and Diffraction of Light 1 Rev 12/19/18 KET Virtual Physics Labs KET © 2019 Explore the Apparatus Open the Interference and Diffraction Lab on the website. The Virtual Interference and Diffraction Apparatus is a very simple device with just a few controls. Monochromatic light from a fictitious multi-color laser passes through one or more vertical slits in an opaque slide. The light arrives at a Viewing Screen 1.00 m away from the slide where it produces an interference pattern. The laser is its own switch. Click it to turn it on. We’ll refer to the table with the Laser, Slits and Viewing Screen as “the apparatus.” Below the apparatus you’ll find controls and display screens. In Figure 1, notice the Viewing Screen, Intensity Graph, and Fringe Display. Be sure that your Laser is turned on and click the Scan Viewing Screen button. A Photodetector moves across the interference pattern on the Viewing Screen measuring the intensity of the light as a function of horizontal position. The intensity vs. position data is displayed in two ways. The intensity is indicated by • the height of Intensity Graph, which is a plot of the intensity of the light vs. position on the Viewing Screen. • the brightness of the bars of light, called fringes, on the small Viewing Screen on the apparatus, and in the enlarged replica of this interference pattern in the Fringe Display below the Intensity Graph. The Contrast Color slider beneath the Fringe Display may be used to adjust the background to make the fringes more visible. Four parameters can be adjusted with sliders or numeric steppers. • The wavelength can be adjusted throughout the typical visible (human) range of 400 nm to 700 nm. • The width of the slits can be adjusted from 20 µm to 160 µm. • The slit spacing, the distance between the centers of adjacent slits, can be adjusted from 250 µm to 500 µm. • The number of slits can be varied from 1 to 5. The first three parameters also have several preset unknown values. You’ll be assigned an “unknown number” – the number which you’ll use to select your unknowns. So if you are told to use your assigned unknown wavelength and your unknown number is 2, you’ll just select “2” with the wavelength stepper. Enter your assigned unknown number here: Two rulers are provided to measure the • slit width and slit spacing. (Zooming in is recommended here.) • position of a minimum or maximum point relative to the central maximum on the Intensity Graph. Each ruler is calibrated in units appropriate to the size of the object being measured. Any changes you make to the apparatus are immediately reflected on the various screens and displays. The only exception is the Intensity Graph, which doesn’t change until you scan the Viewing Screen with the photodetector. The first objective of this lab is for you to observe what happens when light passes through various configurations of slits. This is something that you almost certainly have not done in the classroom because of the nature and small size of the effects we’ll be working with. But with this virtual apparatus, you’ll be able to adjust all the variables that appear in the equations to see their actual roles in the phenomena of interference and diffraction. “Perhaps some gentle persuasion with some sharply pointed questions will encourage you to do some preliminary investigation. We will turn on the laser now. And by we I mean you.” – movie villain of your choice. 1. Drag the wavelength slider all the way to the left. We’ll call this color violet. What’s its wavelength? nm 2. Drag the wavelength slider all the way to the right. We’ll call this color red. What’s its wavelength? nm VPL_Lab - Interference and Diffraction of Light 3 Rev 12/19/18 KET Virtual Physics Labs KET © 2019 For humans there’s a range of wavelengths that could be called red, a range called orange, etc. We, like Newton, find that as we move through the colors from red to violet we come upon about six or seven with widely agreed upon names and hues. His representation of the colors as a continuum doesn’t correspond to any real behavior. And indigo might be a stretch for most of us. 3. It’s useful in our work to know about the order of these colors in the spectrum and how they relate to wavelengths. So, let’s get to know them. Select a wavelength in the range of each color in the sequence ROYGBIV. There are no exact answers. Just aim for a color in the middle of the range. a. Red Figure 2a: From Newton’s Optiks b. Orange c. Yellow (Very narrow) d. Green e. Blue f. Indigo No Way g. Violet (Very narrow) Figure 2b: From Pink Floyd’s Optiks With this apparatus, light from the laser passes through one or more slits and then hits a screen one meter away. In addition to the color of the light, you can adjust the width of the slits, the number of slits, and the spacing between the slits. Try each of these and notice how the enlarged view of the slits on the Fringe Display reflects your changes. 4. Set the laser color to a red, the number of slits to one, and the slit width to 40 µm. Scan. (This means to click the Scan Viewing Screen button.) You should see a nice red “fringe” that takes up about half the width of the Fringe Display. Two other very dim fringes appear just at the edge of the Fringe Display. Adjust the background contrast as needed. Zoom in three times on the Viewing Screen on the apparatus. The Fringe Display just shows the central part of this full, but tiny, display. Zoom back out to 100%. 5. Slowly adjust the wavelength from red to violet. Scan. As the wavelength decreases, the width of the central, bright fringe (increases or decreases) 6. Reset the color to red. Scan. The slit width should be set to 40 µm. Slowly increase the slit width to its maximum value. Scan. What three significant changes do you observe as you increase the slit width? One involves the Intensity Graph. 7. Reset the slit width to 40 µm. Scan. Change the number of slits to two. Scan. Describe the changes in the Fringe Display and the Intensity Graph. Also comment on what stays the same. 8. Feel free to change the number of slits up to 5 and Scan if you like spiky things. VPL_Lab - Interference and Diffraction of Light 4 Rev 12/19/18 KET Virtual Physics Labs KET © 2019 Theory A. Diffraction and Interference While you’re waiting for your opponent to arrive at the tennis court, you can warm up by hitting the ball against a wall. You can count on the ball to behave in a predictable manner. If you have good aim, the ball is always going to bounce back. If you hit it past either side you know right where to go to pick it up. So unless you hit the ball over the wall, the area behind the wall is a tennis ball shadow. If you do hit the ball over the wall and some kind person on the other side throws it back over the wall to you, you don’t have to climb the wall or walk to the edge of the wall to shout your thanks. Not only can you just shout toward the wall, you can shout in almost any direction and still be heard. Clearly sound doesn’t behave like a tennis ball. There is no sound shadow behind the wall. There are actually two phenomena involved in this “hearing around corners” phenomenon. When the sound arrives at an edge of the wall, it bends around the wall. This “bending” of waves when they reach an opening or an edge is called diffraction. So how does the sound get behind the wall when you don’t even shout in the direction of the wall? It diffracts when it exits your mouth. Differently shaped speakers for different situations and cheerleading megaphones suggest that there are ways of modifying the amount and direction of diffraction. There’s another factor involved in talking to someone behind the wall. If you or your listener were to move around a bit you’d find that the sound heard would be clearer and louder at some points and more garbled at others. This is because all this sound wrapping around and over the wall is recombining at your listener’s ears to reproduce the pattern of compression and decompression of the air that you originally produced. Sound coming by different paths will be out of sync to different degrees, so what’s heard is a mash up of different parts of “Thank you very much for returning the ball.” Something like: “Thank you very much for returning the ball.” → “Thank you very much for returning the ball.” → “Thank you very much for returning the ball.” → “HUH? All I got was a bunch of noise ending with bbball” The merging together of these sound waves to produce one sequence of compressions and rarefactions that you’re trying to interpret is called wave interference. Once the sounds split into several paths, the geometry has to be just right to get them back in sync. It’s no wonder that marching bands are impossible to hear clearly. The sound is diffracting in all directions when it leaves their instruments, and then it reflects off of a sloping wall of people and concrete to get to your ears! In summary, multiple waves arriving at a given point combine to produce a resultant wave, which is the sum of the amplitudes of the various waves. This is the process of interference. That seems pretty tidy. We have diffraction and interference. But, well, diffraction involves interference. As Dr. Feynman pointed out in the opening quote, there is not a clear distinction between interference and diffraction. Physicists have gotten accustomed to being very loose with these terms, and it seems to be beyond fixing. We’ll first look at cases of pure interference of waves and then explore interference resulting from diffraction. (See, there’s a good example of the loose use of these terms. It’s a typical and acceptable example of their use, but confusing if you’re trying to understand the difference in their definitions. See Dr. Feynman’s opinion on that.) We’ll also find that several factors can be important. An equally loud bee buzzing in front of the wall will not be as easy to hear behind the wall. Wavelength matters. You’ve already done the research to understand that one in the introduction. The high frequency (shorter wavelength) blue diffracts – bends around corners – less than the low frequency (longer wavelength) red light. Similarly, the high frequency bee would be harder to hear behind the wall. VPL_Lab - Interference and Diffraction of Light 5 Rev 12/19/18 KET Virtual Physics Labs KET © 2019 B. Interference Let’s look at the interference of a pair of waves on the surface of a tank of water. Figure 3 is a snapshot of a red marble jiggling up and down when partially submerged in a tank of water. A continuous circular surface wave is produced. The small bit of Styrofoam jiggles up and down with a slight delay due to the travel time of the wave. Figure 3: Water Waves In Figure 4a, the small red (top) and blue (bottom) dots at the left represent a pair of marbles jiggling similarly. (Overhead view.) They are moving in phase. That is, they are at all times at the same height and moving in the same direction. Each time they strike the water a new trough is produced. Half a period, T, later the water will overshoot its equilibrium level and ! produce a crest. The circles represent wave crests. Troughs would be found half-way between adjacent crests. In Figure 4b, " later, each wave has traveled a distance equal to half a wavelength. So each crest has reached a point previously occupied by a trough. Each of the four circular viewports in each figure shows an edge-on snapshot of the water wave at the point it connects to. The top and bottom viewports, (i), and (iv), show regions where only one of the two waves has arrived. As the actual water waves move over time, the waves in these viewports would move left to right across the cross-hairs. Notice how from Figure 4a to Figure 4b, each of these snapshots shows the wave moving a distance equal to half a wavelength. A crest is shown at the center of the cross-hairs in Figure 4a and the following trough is centered in Figure 4b. The middle pairs of viewports, (ii), and (iii), show the waves at two points where they have already overlapped. In this region, at a given instant, the wave height at any point is the sum of the heights of the individual waves passing through that point, at that instant. The individual waves have lost their individual identities. Viewport (ii) in Figure 4a shows that at the point it refers to the water is a double-depth trough. In Figure 4b, it indicates a double-height crest. These waves will always be in phase at this point, which means they will always be at the same point in their cycle of up and down motion. At this instant, their resultant wave has twice their individual amplitudes. This addition of amplitudes where both waves are displaced in the same up or down direction is called constructive interference. This effect is at its maximum at this instant since both waves are at maximum points in their cycle. The waves were created in sync and each has traveled 4.5 wavelengths to arrive at the fixed point where the snapshot is being taken. (4a) In Phase – Trough (4b) In Phase – Crest (4c) Nodal and Antinodal Lines Figure 4: Interference of Two Overlapping Circular Waves In viewport (iii), we see the opposite effect. Again the waves start out in phase, but in Figure 4a, the red (top source) wave has traveled 5 wavelengths but the blue (bottom source) wave has traveled only 3.5 wavelengths. And in Figure 4b, each has traveled another half wavelength but, at the fixed point we’re observing, they are still exactly out of phase. Thus the waves are exactly out of phase and will remain that way over time. This out-of-phase addition is called destructive interference. VPL_Lab - Interference and Diffraction of Light 6 Rev 12/19/18 KET Virtual Physics Labs KET © 2019 Further inspection shows that all points along the dashed centerline will experience double-height crests and troughs. In Figure 4c, the top and bottom dashed lines have been drawn passing through intersections of waves where they are in phase. All points along these lines will also experience alternating double-height crests and double depth troughs. The other pair of dashed lines connect points where troughs of one wave intersect with crests of the other wave. Again, the waves “cancel” leaving approximately still water. These lines of constructive and destructive interference alternate. You’ll see later that the spacing, and hence the number of lines that appear, depends on the spacing of the wave sources and the wavelength. Figure 5 shows an actual photograph of this wave pattern. If you were to sit in an inner tube anywhere along one of five thin antinodal lines you’d be subjected to large up and down motions as large crests and troughs arrive in succession. Sitting in your inner tube anywhere along the one of the four thick nodal lines is a fairly calm experience. The waves approximately cancel out to the level of still water. Hopefully you can clearly see how this behavior parallels the behavior of the light hitting our Viewing Screen. The bright points are equivalent to the ends of the antinodal lines in Figure 5. What we’ve seen so far with water waves is also found with other types of waves such as sound and light waves. We’ll consider the particular case of light from here on. Constructive interference will produce bright fringes on a screen while destructive interference will produce dark fringes. Figure 5: Nodal and Antinodal Lines in Water; Bright and Dark Fringes On a Screen You’ve already observed this pattern of bright and dark fringes in your initial exploration with the apparatus. The same geometry that produces these effects provides a framework for a mathematical description of this behavior. Equations for the location of nodal (dark) and antinodal (bright) fringes We’ve found that points of constructive or destructive interference are due to the difference in distance, the path difference, Δr, between the sources and positions on a screen. (This assumes that the sources are in phase which they’ll always be with this apparatus.) Specifically, if light travels λ, 2λ, 3λ, etc. farther from one source than from another, then constructive interference will occur. Similarly, destructive interference will occur if the path difference is 0.5λ, 1.5λ, 2.5λ, etc. In Figure 6, light sources S1 and S2 produce identical waves in phase. Since r1, and r2 are equal distances, all waves will arrive at point P in phase. Crests will arrive together, as will troughs. So point P will be a bright fringe. Due to the symmetry of the arrangement, we would call it the central bright fringe. This corresponds to point (ii) in Figures 4a-c. Figure 6: Central Bright Fringe If we examined other points along the screen, we’d find a first pair of bright points equal distances above and below the original point P. Figure 7 shows the two new paths taken to reach one such point, P. Both paths are longer than before, but they are no longer equal. The path from S2 to P must be exactly λ further than the path from S1 to P. # Between the central bright fringe at O and the next bright fringe at P will be a dark fringe at a point where r2 – r1 = . " VPL_Lab - Interference and Diffraction of Light 7 Rev 12/19/18 KET Virtual Physics Labs KET © 2019 Figure 7: First Order Bright Fringe Figure 8: First Order Bright Fringe, where L ≫ d Imagine a screen much farther to the right. For θ to remain the same, y would have to be proportionally larger. And at a great enough distance, L, the lines labeled r1 and r2 would be approximately parallel as shown in Figure 8. (This figure is enlarged.) There is no change in the value of d.) In this case, where L ≫ d, the mathematics is much simpler than what we see in Figure 7. We’ll just deal with this case, which was developed by Joseph Fraunhofer. (See the “Cosmos: A Spacetime Odyssey” "Hiding in the Light" episode to see how we almost lost young Joseph. He was fortunate to have a house fall on top of him.) For this case, the angle θ between r1 or r2 and L will be the same as the angle θ in the right triangle shown in Figure 8. For the first bright fringe, we found that the path difference, Δr = λ. For the n ...
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Final Answer

Attached.

Diffraction and Interference of Light Lab
Introduction
Diffraction and interference of light are phenomena that arise under particular conditions. According
to Dr. Feynman, a clear distinction between diffraction and interference is yet to be attained.
Diffraction can be conceptualized as the bending of waves e.g. light and sound waves when they
reach an edge or opening. Interference is the process that involves combination of multiple waves
reaching a given point to yield a resultant wave which sums the amplitudes of several waves. Light
which forms part of the electromagnetic spectrum is propagated as a wave and as a result exhibits
diffraction and interference phenomena. Laser light shone through a small hole forms a pattern 0f
dark and bright spots instead of a single spot. Wavelength property of waves is important as far as
diffraction is concerned. Blue light which has shorter wavelength tends to bend around edges and
corners less compared to red light which has longer wavelength. This lab uses laser light to
investigate diffraction and interference phenomena.
Purpose of Lab







To observe the behavior of light passing through various configurations of slits.
To investigate how the width of a slit and the wavelength of the light passing through it
determine the diffraction of light.
To determine the wavelength of laser light from the diffraction pattern produced when it
passes through a single slit.
To determine the wavelength of laser light from the interference pattern produced when it
passes through a pair of slits.
To measure the width of a narrow slit from the diffraction pattern produced when laser light
passes through it.
To investigate the role played by single slit diffraction in the variation in intensity of a double
slit interference pattern.

Hypothesis (Expected Results)
When light passes through a slit, it is expected to be and spread as they pass through it. In the case
of two or more slits, the light waves will combine to attain new amplitudes through what is
described as interference producing dark and bright fringes on the screen.
Background
Interference
When two different waves meet at a point in space the combine resulting in new amplitudes. When
the two meeting waves are in phase, they add constructively forming a bright spot. In a case where
they are out of phase, they destructively add forming a dark spot. The two cases are illustrated in
Figure 1.

Figure 1: Constructive and Destructive Interference
Two Slit Interference
When the laser light hits the two slits, they act like in-phase point light sources. The light from the
two slits to a point in the screen travel different distances. For example, for a point P as shown in
Figure 2, light from the bottom slit travels a longer distance than the top slit. The extra distance is
responsible for introducing a phase shift between the two waves resulting in a position dependent
interference pattern casted on the screen.

Figure 2: Double Slit Interference
Through derivation, Equation 1 and 2 can be obtained. For small angles, the value of sin 𝜃𝑚 and

tan 𝜃𝑚 are almost equal. Therefore, equating Equation 1 to Equation 2 and making 𝑦𝑚 the
subject of the formula yields Equation 3.
sin(𝜃𝑚 ) =
tan 𝜃𝑚 =
𝑦𝑚 =

𝑚𝐿𝜆
𝑑

𝑚𝜆
𝑑

𝑦𝑚
𝐿

…………………………………….………...

Prof_Axel (1725)
University of Virginia

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