Online reading assignment: double-slit interference

Physics 205B, spring semester 2020
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on double-slit interference.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"For in-phase sources, the difference in path length will be a whole number of wavelengths for constructive interference. For destructive interference the path difference will be (a whole number plus) a half of a wavelength."

"The presentation did a good job at conveying the path differences for the double slits. It was defined clearly."

"I understand from this section that the maxima and minima of a double-slit interference means whether or not it is constructive or destructive. this is determined by various variables of a double-slit interference like the wavelength, distance between slits, etc."

"Young's double-slit experiment showed how two monochromatic light sources could interfere constructively and destructively. This was shown by the alternating dark and light fringes on the screen he used."

"The difference in lengths that parallel waves travel is equal to their separation distance d between multiplied by sinθ. The inner wave also travels farther."

"In double-slit interference θ is measured from the horizontal and ranges from –90° to +90° with 0° deg being horizontal. The equation dsinθ is used to find the difference in path lengths traveled by two sets of waves. Whether the resulting wave is constructive or deconstructive depends on the whether there is a whole or and a half difference in path lengths."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Maxima and minima were confusing. double-slit interference was more difficult to understand."

"Definitely the picking the correct information to match the equation. All these symbols are confusing."

"The 'Train of Pain' is still a little confusing, just need to a little more with it."

"I understand the equations and the idea of the path lengths pretty well, but I might need some more practice using and applying them."

"I would benefit from homework examples that have to do with calculating the maxima and minima values to acquire a greater understanding of their relationship to the central bright spot."

"I pretty much understood everything, especially the basics. I might need some polishing of some concepts but that's it."

"Nothing at this time."

Explain the difference between "maxima" and "minima" in double-slit interference.

"The resulting constructive interference is the maxima, and the resulting destructive interference is the minima."

"A maxima is where it is brightest and a minima is where it is least bright."

"Maxima refers to the bright fringes while minima refers to the dark fringes."

Match the double-slit parameter with its symbol. (Only correct responses shown.)

Distance between slits: d [74%]
Any positive or negative whole number: m [74%]
Distance from slits to a projection screen: L [49%]
Wavelength of light passing through both slits: λ [83%]
Difference in paths for light passing through both slits: d·sinθ [51%]
Position along screen, as measured from the centerline: y [46%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [97%]
Path difference: integer number of wavelengths [100%]
Interference: constructive [97%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [89%]
Path difference: odd number of half wavelengths [94%]
Interference: destructive [94%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [97%]
Path difference: integer number of wavelengths [77%]
Interference: constructive [74%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Would like to review these last two diagrams in or after class."

"Are you going to go over this in class?" (Yes.)

"Will we be doing the double-slit experiment in lab?" (Yes.)

"Since the light that passes through the double slits is from a source that is side-by-side and in-phase with the same wavelength, won't the light passing through the two slits always be in phase?" (Well, yes, unless one wave has to travel a further distance than the other wave in order for them to meet at a receiver.)

"I'm not sure how to use the formula ∆l = dsinθ. In which case will the path difference be a whole wavelength or half a wavelength?" (Well, just calculate ∆l for a given θ direction, then see if it is equal to m·λ or (m + 1/2)·λ.)

"I think that in regards to Young's double-slit experiment, when two light paths interfere constructively they create a bright fringe, and when they interfere destructively they produce a dark fringe... is that correct?" (Yes.)

"I was a little confused whether the double-slit experiment only works when the light sources are side-by-side. If you have two separate sources of light that are constructive but that differ in distance does the double-slit experiment still work?" (Yes, but the sources must have exactly the same wavelength, and be in phase with each other. For visible light the most practical way to do this is to have a laser illuminate two side-by-side slits simultaneously.)

"I would benefit from some practice problems."

"Going to try my hardest to make it tomorrow."

Online reading assignment: double-slit interference

Physics 205B, spring semester 2019
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on double-slit interference.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"How the maxima and minima angles can give us constructive or destructive interference."

"Constructive interference leads to a bright fringe. Destructive interference leads to dark fringe. Intensity varies among the bright fringes; the central fringe has the greatest intensity."

"For two waves with in-phase sources and a distance of d apart from each other, we can approximate their path length difference by using the formula d·sinθ measured from the center line."

"When two waves are leaving from separate slits in phase they can be traveling parallel where θ = 0° and they would stay in phase. If the angle at which both waves are traveling is not zero then one wave is traveling a longer distance and thus can make the waves destructive interference. Constructive or destructive interference depends on how far apart the waves are from each other and the angle at which they are going toward the object."

"A detector can be used to detect the interference between two in phase sources that are side-by-side. The sources interfere at a detector that when moved side to side, create a path difference of the sources that can detect whether the sources interfere constructively or destructively. As the angle that the waves are moved changes, either by half a wavelength or a whole wavelength, the interference changes. "

"When light from two in-phase sources pass through slits, the two 'path lengths' of light from the slit to the point where they meet can relate in two important ways. If the lengths are equal or differ by a whole wavelength, constructive interference will occur when the two lightwaves meet and form a maxima. If the lengths differ by half of a wavelength, destructive interference will occur when the lightwaves meet and form a minima."

"Honestly I'm still kind of lost on this. I know we are looking for the difference in path length, but the equations are a bit difficult."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I'm a little confused on what the variables are and how they relate to the pictures in the presentation."

"I don't understand the connection between maxima/minima angles and interference."

"I'm still not quite sure about what minima and maxima mean and how that related to constructive and destructive interference."

"I found the double-slit interference to be a little confusing where m is used as an integer used to describe how many wavelengths difference the waves are. It was confusing at first but after thinking it through and a little practice it made a lot more sense."

"I find it hard to understand the equations. Perhaps a tutorial in class may help."

"How do we know when to use each path length difference equation for the maximas and minimas?"

"I need practice applying the ∆l = d·sinθ equation. I also need to better understand the principle of a diffraction grating."

"Not confused much but would like to see examples."

"I am still a bit confused about how to apply the path length difference approximation in problem-solving. I feel like I understand the principles, different waves are interfering, but I do not understand why this is useful."

"Might be some confusion on putting all the pieces together."

"Not too much is super-confusing to me."

"I didn't really find anything very confusing I think I've got a pretty good understanding of the material. "

Explain the difference between "maxima" and "minima" in double-slit interference.

"'Maxima' refers to constructive interference and 'minima' refers to destructive interference, regarding double-slit interference of in-phase waves."

"Maxima is dark and minima is bright."

"It seems that maxima is a constructive interference and the minima is destructive."

"No idea--but I know calculus maximas and minimas."

Match the double-slit parameter with its symbol. (Only correct responses shown.)

Distance between slits: d [85%]
Any positive or negative whole number: m [85%]
Distance from slits to a projection screen: L [67%]
Wavelength of light passing through both slits: λ [92%]
Difference in paths for light passing through both slits: d·sinθ [54%]
Position along screen, as measured from the centerline: y [62%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [95%]
Path difference: integer number of wavelengths [87%]
Interference: constructive [97%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [74%]
Path difference: odd number of half wavelengths [82%]
Interference: destructive [90%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [90%]
Path difference: integer number of wavelengths [67%]
Interference: constructive [79%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"No question today, this all seems to make sense to me."

"How did I do on my ray tracings for the quiz?" (Have you checked your quiz scores online?)

"This was very helpful in making the path length differences and how the two wavelengths form the light and dark spots 'click' for me."

"Is there a way to mathematically check these examples above?" (Before every class, click on the "review previous reading assignment responses" link to see the correct answers for each reading assignment question.)

"I'd like to know how to do the interference from the path length differences." (You'll get to see this in lab.)

"Okay this might be dumb but I don't really understand what the double-slit interference is. I don't understand what this interference is supposed to represent." (It's a way of dividing a single beam of light into two (or more) separate beams of light, that can interfere with each other constructive (or destructively) in certain directions. Next week's lab is where we shoot a laser beam through a CD-RW disc, such that it passes through many adjacent tracks to separate into many separate beams of light that will interfere constructively (or destructively) at certain places on a screen.)

"Sometimes I get tripped up on the math, so the trigonometry confuses me a bit. I would love to see something drawn to scale where the parallel lines from the two slits end up creating a bright spot together." (We'll get to "act out" how two waves interfere constructively or destructively for double-slit interference.)

"Is there any way you can make the individual lab reports less time consuming and tedious, especially the procedure section? :(" (Although the procedure section can get tedious if you detail every step that you did in lab, there is a skill in summarizing that in a succinct manner (usually with diagrams) that I would like you to practice this semester. Shorter is better, but not too short.)

Online reading assignment: double-slit interference

Physics 205B, spring semester 2018
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on double-slit interference.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"The general introduction to double-slit interference; more specifically the modified 'Train of Pain.'"

"We are able to find out if constructive or destructive interference occurs at a detector when two in-phase light waves are situated so that they are offset at an angle, which therefore also produces a difference in length. We can use an equation to find maxima/minima, angle, and length as they are related to each other."

"When comparing two waves that are both in phase, we're trying to figure out how much longer it takes for one wave to travel than the other. The path difference, how many wavelengths, etc."

"When considering path differences we can make the assumption that the detector is sufficiently far from the source of waves and that the two waves (d apart) travel along a parallel path. This makes it so that the location of the detector can be specified by a specific angle."

"Double-slit interference is basically a case in which waves from two side-by-side in phase sources interfere in both a constructive or destructive manner. In this lecture, source phases do not matter since we are looking at only in-phase sources, so our main focus of attention is looking at the path differences. The minima are where the paths interfere destructively, and the maxima are where the paths interfere constructively. There exists a trigonometric equation to determine how long a path is relative to another path as well."

"When comparing two waves that are both in phase, we're trying to figure out how much longer it takes for one wave to travel than the other. The path difference, how many wavelengths, etc."

"When we change the path of two waves, it affects the distance the waves have to travel to reach a destination. The equation delta ∆L = d·sinθ will tell if the interference is constructive (maxima) or deconstructive (minima)."

"The maxima and minima angles can give us constructive or destructive interference. This interference could be the product of waves having a path difference of a whole or half wavelength."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"Nothing was really confusing so far. I think the only thing harder to understand for me was the diagrams and the angle itself how that is found."

"How the altered distance of the two parallel waves effects their in/out of phase properties."

"I need more help on applying the ∆L = d·sinθ equation."

"I seemed to have understood this alright. Some lecture time would help me though."

"I'm confused about when a path difference would be destructive. My assumption is that the waves are constructive when the angle is at 0 degrees and destructive when the angle is larger or smaller than zero because these cases require that one path be shorter than the other."

"The path difference is really confusing to me. I think because it is harder to 'picture' in my head as I think it out."

"I don't understand the principle of a diffraction grating."

"Could you go over the equations?"

"I really don't find this presentation confusing. But how do we know and test which angles will be destructive and constructive?"

"I was pretty lost on finding the maxima and minima. I understood how you can manipulate delta l to be able to plug in wavelengths and m and then solve for an angle theta, but I don't know how this angle really comes into play in the big picture of it all."

"I really don't understand how path length differences are calculated."

"I didn't find anything too confusing in this lesson."

Explain the difference between "maxima" and "minima" in double-slit interference.

"'Maxima' is constructive interference and 'minima' is destructive interference."

"When two in-phase sources in a double-slit interfere at maxima this is constructive interference, and when they interfere at a minima there is destructive interference."

Match the double-slit parameter with its symbol. (Only correct responses shown.)

Distance between slits: d [74%]
Any positive or negative whole number: m [83%]
Distance from slits to a projection screen: L [55%]
Wavelength of light passing through both slits: λ [97%]
Difference in paths for light passing through both slits: d·sinθ [62%]
Position along screen, as measured from the centerline: y [55%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [100%]
Path difference: integer number of wavelengths [97%]
Interference: constructive [97%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [61%]
Path difference: odd number of half wavelengths [94%]
Interference: destructive [94%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [90%]
Path difference: integer number of wavelengths [74%]
Interference: constructive [84%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Review the above three diagrams from this assignment?"

"I could never go wrong with some more practice with the types of problems above, hopefully we have some in class :) ?"

"What is y? I put 'position along the screen as measured from the centerline.' Not sure I see what we are talking about."

"I am sorry I could not think of anything funny to write or ask this time, I will do better next time I promise.

Online reading assignment: double-slit interference

Physics 205B, spring semester 2017
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on double-slit interference.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"I know the difference between maxima and minima."

"That the path length difference relation tells us where the maxima or minima will be."

"With the double-slit interference, the source phase differences don't matter, but that just their path differences do, we are wanting to know how much longer the wave from one source travels than the wave from the other source. I also understood that in a double-slit interference condition the constructive is maxima, and a condition that is destructive is minima."

"Double slit interference is two side-by-side in-phase sources. Phase differences don't matter with this and only the path matters. When calculating this we locate where these two sources interfere constructive (maxima) or destructively (minima)."

"A really small difference in distances can put waves in interference with each other; it is interesting how much of a difference it can be."

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I am not understanding the flow chart for the constructive and destructive conditions. How am I able to tell which pathway I am to choose for the condition I am given?"

"How to figure out the difference between the minima and maxima for double-slit interference."

"Path length differences. I'm just not fully understanding on how to find it."

"I don't really understand what double-slit interference is."

Explain the difference between "maxima" and "minima" in double-slit interference.

"Constructive interference is maxima and minima is destructive interference."

"The difference between the two is that the maxima is when there is a constructive interference or when the path difference is a multiple of the wavelength. A minima happens when there is a destructive interference or when the path difference is either an odd number of half wavelengths."

"No idea."

"I'm trying to understand it."

"Maxima and minima is the minimum and maximum of wavelength?"

Match the double-slit parameter with its symbol. (Only correct responses shown.)

Distance between slits: d [77%]
Any positive or negative whole number: m [77%]
Distance from slits to a projection screen: L [41%]
Wavelength of light passing through both slits: λ [100%]
Difference in paths for light passing through both slits: d·sinθ [50%]
Position along screen, as measured from the centerline: y [46%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [95%]
Path difference: integer number of wavelengths [91%]
Interference: constructive [91%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [59%]
Path difference: odd number of half wavelengths [86%]
Interference: destructive [77%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [73%]
Path difference: integer number of wavelengths [82%]
Interference: constructive [68%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"Can we discuss the difference between maxima and minima in double-slit interference?

"Do we call it maxima/minima only when we're talking about interfering waves?" (Well, yes, but this works for both interfering sound waves (loud/quiet regions) or interfering light waves (bright/dark regions).)

"Petition for more long weekends!"

"Did you ride any emus over the long weekend?" (No, but Mrs. P-dog and I went snowshoeing up in the mountains.)

Online reading assignment: double-slit interference

Physics 205B, spring semester 2016
Cuesta College, San Luis Obispo, CA

Students have a bi-weekly online reading assignment (hosted by SurveyMonkey.com), where they answer questions based on reading their textbook, material covered in previous lectures, opinion questions, and/or asking (anonymous) questions or making (anonymous) comments. Full credit is given for completing the online reading assignment before next week's lecture, regardless if whether their answers are correct/incorrect. Selected results/questions/comments are addressed by the instructor at the start of the following lecture.

The following questions were asked on reading textbook chapters and previewing presentations on double-slit interference.


Selected/edited responses are given below.

Describe what you understand from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically demonstrate your level of understanding.

"Paying close attention to the diagrams. We're looking at waves at various angles to see how it affects interference."

"When there is two side-by-side in phase wave sources--because the wave sources are in phase, what we are concerned about in this case are path differences only. In double-slit interference a condition that is constructive is maxima, and a condition that is destructive is minima."

"Since light is a wave it travels through slits creating dark areas and bright areas depending on how it has interfered with other waves of the same wavelength."

"NOTHING! HELP!"

Describe what you found confusing from the assigned textbook reading or presentation preview. Your description (2-3 sentences) should specifically identify the concept(s) that you do not understand.

"I don't understand the logic of path length differences. I'm not sure how to how to explain or walk through setting the equation up."

"This seemed pretty straightforward, even from just skimming it."

"I don't get how this is mathematically quantified."

"I am having trouble on deciding if something is in phase or out of phase. Also another thing i am not understanding is if it is destructive or constructive. I tried the chart from the previous blog but i am still a little bit confused."

Explain the difference between "maxima" and "minima" in double-slit interference.

"Maxima are points of constructive interference, and minima are points of destructive interference."

"Maxima is the location where light from two individual sources are reinforcing each other and correspond to points of brightness. Minima as where two individual sources are destroying each other and correspond to points of darkness."

"Meow."

"Minima = constructive interference, maxima = destructive interference."

Match the double-slit parameter with its symbol. (Only correct responses shown.)

Distance between slits: d [64%]
Any positive or negative whole number: m [82%]
Distance from slits to a projection screen: L [41%]
Wavelength of light passing through both slits: λ [86%]
Difference in paths for light passing through both slits: d·sinθ [50%]
Position along screen, as measured from the centerline: y [50%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [94%]
Path difference: integer number of wavelengths [78%]
Interference: constructive [89%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [53%]
Path difference: odd number of half wavelengths [56%]
Interference: destructive [72%]

Identify the characteristics of the sources, path difference, and interference type. (Only correct responses shown.)

Sources: in phase [83%]
Path difference: integer number of wavelengths [50%]
Interference: constructive [56%]

Ask the instructor an anonymous question, or make a comment. Selected questions/comments may be discussed in class.

"I didn't think you could add angles into this topic. How do we determine the angle off to the side of the dashed center line? Will it just be given or should we know how to find it?" (Typically there are three related parameters: slit spacing d, maxima (or minima) angle θ, and wavelength λ. If you are given any two, you should be able to solve for the third.)

"I get the constructive/destructive subway map. That's cool." (Cool. Cool cool cool.)

"Everything is confusing and overwhelming at this point. I'm hoping none of this stuff is on Quiz 2 or else I'm in major trouble!" (Quiz 2 only covers lenses, interference is on Quiz 3.)

""These assignments are a lot harder to do when you haven't had time to read the book."

"What would happen if the detector moved from θ = +23° to θ = –23°?" (It would still be destructive interference, as the diagram would just be flipped. #isitworthit #letmeworkit #iputmythingdownflipitandreverseit)

"Missy Elliott has been stuck in my head since Monday. Thanks P-dog." (#tiesreverdnatipilfnwodgnihtymtupi)

Presentation: double-slit interference

Here we have microwaves (as discussed previously, a long wavelength form of electromagnetic radiation) from two side-by-side in-phase sources, interfering at a detector that can be moved at various locations to detect their interference, whether constructive or destructive (as translated into an audio signal). (Video link: "MIT Physics Demo--Microwave Interference.")

In the previous presentation we discussed the conditions for constructive or destructive interference for waves (of the same wavelength) due to phase and/or path differences. In this presentation we discuss the very specific case of waves (again, of the same wavelength) from two side-by-side in-phase sources, which we will see has been classically called "double-slit" interference.

First, path-length differences.

The waves we are considering will come from two sources that are in phase, so we do not need to concern ourselves with the out of phase sources. Since source phase differences don't matter here--only path differences--then we must pay careful attention to the difference in path length: how much longer the wave from one source travels than the wave from the other source, as they reach and interfere at the position of the detector, as it moves from side-to-side.

We are going to make the assumption that the detector is sufficiently (approaching infinitely?) far away from the two sources (spaced apart by a distance d) that the two waves will travel along a parallel path 1 and path 2. Then the location of the detector can be specified merely by the angle θ (where θ = 0° would be on the center line).

In this case, for the angle θ shown, waves travel longer along path 2. How much longer the waves travel along this longer path can be given by the relation ∆l = dsinθ. (There is a trigonometry derivation using the right triangle for this relation, but the focus here is on relating ∆l with the resulting constructive interference (maxima) or destructive interference (minima), and later on during problem-solving we'll use the ∆l = dsinθ relation to find these maxima and minima θ angles, without worrying too much about how to derive this ∆l = dsinθ relationship.)

Here's the simple case (θ = 0°) where both waves leave their slits to travel equal distances to the distant detector towards the right. Do the waves start from their slits in phase or out-of-phase? Is the path difference a whole wavelength or a half-wavelength? Does constructive interference (maxima) or destructive interference (minima) occur at the detector?

In this case, both waves leave their slits to travel unequal distances to the distant detector towards the right, located at an angle of θ = +23° off the (dashed) center line, such that path 1 is shorter than path 2. Do the waves start from their slits in phase or out-of-phase? Is the path difference a whole wavelength or a half-wavelength? Does constructive interference (maxima) or destructive interference (minima) occur at the detector? What would happen if the detector were instead placed at θ = –23° (same angle but on the other side of the center line)?

Now in this case, both waves leave their slits again to travel unequal distances to the distant detector towards the right, located at an angle of θ = –51° off the (dashed) center line, such that path 1 is longer than path 2. Do the waves start from their slits in phase or out-of-phase? Is the path difference a whole wavelength or a half-wavelength? Does constructive interference (maxima) or destructive interference (minima) occur at the detector? What would happen if the detector were instead placed at θ = +51° (same angle, but on the other side of the center line)?

Second, where we are going with this path-length difference relation: locating where these two sources interfere constructive (maxima) or destructively (minima).

As discussed before, for in phase sources, the difference in path length will be some integer m multiple of a wavelength for constructive interference, or will be some integer and a half (m + 1/2) multiple of wavelength for destructive interference.

So now let's put in our approximation for the path difference ∆l = dsinθ, for two waves from side-by-side sources reaching a (distant) detector located at an angle θ. What we will wind up with is a relation between the angle θ that a distant detector is located at, and the condition for either constructive (maxima) or destructive (minima) interference to occur. So given the wavelength λ of the two side-by-side sources, and the separation distance d between the two side-by-side sources, then plugging in different integer m values (0, ±1, ±2, ±3, etc.) allows us to solve for different θ angles where either constructive (maxima) or destructive (minima) interference occurs.

You will demonstrate this for yourselves in recreating a classic experiment in laboratory. Using laser light (of a given wavelength λ) that illuminates two very closely spaced together slits (two in-phase sources spaced a distance d apart), there will appear bright (maxima, or constructive interference) regions and dark (minima, or destructive interference) regions on a screen (the detector) at certain θ angles, as predicted by the double-slit interference maxima/minima equations.