# Talk:Snell's Law

Response to the Checklist.

• Messages to the Future

I don't really have suggestions of material for future. If someone wants to write about mirrors I think that would be really cool. They can talk about ray tracing and the math behind how you may see things differently based on their position, location and size. I guess this goes into the ray tracing I was going to include. It's somewhat similar but can be an entire new page as well.

References and footnotes

• All images are properly attributed.
• I modified some pictures and made some of my own.
• No direct quotes from textual sources were used.
• References for text are at the end of the page.

Good writing I think the page makes is clear why the topic and specific mathematical content of the page are useful. I try to define the topic or purpose of the page as a whole. the heaviest math is placed as late as possible within this section. I provided a easy derivation and a harder one later one.

• I think one other addition to the "why it's interesting" section would be an explanation of how snell's law is actually the underlying principal behind anything that uses lenses (your eyes, glasses, cameras, microscopes, etc). A paragraph on that could help a lot to add more to that section. I'd say it's the most important thing about Snell's Law.

Integration of Images and Text

• I give an explanation of images and instruct the reader where to look.
• I think when you say "In Image 2 this is not the case." early on, you mean image 3.

Fixed this mistake. .

• Can you make image 6 bigger and more clear? It's hard to see what's going on.

Going to edit picture and repost it. .

Connections to other mathematical topics

• page links to basic trigonometric functions a few times in case anyone wants to look up sine.

Examples, Calculations, Applications, Proofs

• I provide numerical examples/problems/exercises. So that the reader has a chance to stop and think. But I also put in the answer in a hide show format.
• I define the law using both numerical values and a word description.
• I provided two proofs that come along with images.
• The application section would be the exercises and also in the why it's interesting section.
• When you say "To minimize the time we take the first derivative and set it equal to 0. " make sure you specify which variable you're using to take the derivative. Alternatively, you could describe the time as t(x) instead of just t

I changed this. . Mathematical Accuracy and precision of language

• The goal is always that all statements, equations, and mathematical terminology are free of errors.
• I also put a quick summary showing exactly what's happening in each step.
• This step: $t_t ' = \frac{\sin \theta_1} {v_1} = \frac{\sin \theta_2} {v_2}$ isn't accurate. What you want instead is $t_t ' = \frac{\sin \theta_1} {v_1} - \frac{\sin \theta_2} {v_2} =0$ which gives the desired $\frac{\sin \theta_1} {v_1} =\frac{\sin \theta_2} {v_2}$. Once changing that, you want to remove the t'= from each of the subsequent lines.

I have changed this. .

Layout

• Text is in short paragraphs, try to make them 100 or less.
• Hide and mouse-over features are used. (I used it in the why it's interesting section to hide the math in case someone just wants to hear about total internal reflection and not see what's going on. )
• Speaced out images and text so things don't clutter. I think the white space in between isn't that large.
• I'd make this sentence bold: "Wave frequency does not change as the wave goes from one medium to another, but the wavelength does change." or do something to make it stand out more.

I put this in boldface. .

## Contents

• Kate 17:27, 6 July 2011 (UTC): Ok, so I took physics in high school, but it was a terrible class and I barely understood any of it, so I thought I'd give you some feedback from the perspective of someone who doesn't know or like physics.
Your unhidden stuff is clear, but if I was just browsing, I probably wouldn't have read the hidden section. That's largely due to the fact that it's pretty much all physics and I just don't like physics, but I think your MME is also less clear than your Basic Description. I don't think you need to dumb it down or anything, you should be writing the section for someone who has a bit more physics than me anyway, but I think a little bit more outlining/sign-posting/telling the reader what you're doing in each section would be a good idea, and I pointed out a couple sections where you might want to go over the wording of your explanations with someone who understands what you're trying to say.
• Ljeanlo1 15:50, 13 July 2011 (UTC) Alright, that sounds like good feedback to me. I'll work on trying to make things a bit more understandable. For the math section I'll give a mini summary before I do any steps. So, hopefully that will help.
Anyway, I think you've got a really good start here. You did an especially good job of defining your terms in the basic description - clear and concise.

• Dayo 16:53, 28 June 2011 (UTC) I would try to change the second sentence of the image description up top. It seems a bit awkward.

Ljeanlo1 15:50, 13 July 2011 (UTC) Is it still awkward now? If so, what do you suggest?

I really like the page though, and think its' a good topic. If having too much physics is the problem I would try to say more about images or how it effects images (which it really does!) "The snell's law on the beach section": it's a really cool application, but I would try to put it under a different heading, maybe an, "applications and examples" section.

Ljeanlo1 15:50, 13 July 2011 (UTC) No, I want the Snell's Law on the beach to lead into the idea of Fermat Principle and the derivation. It's just a quick analogy so that people can understand that light travel in the least time. I did provide examples later on and the application is more in the why it's interesting section.

• xd 14:25, 22 June 2011 (UTC) Is this too much physics? Of course. You are writing about a law in physics on Math Images Page. But if you want to continue this page, you have live with this. In addition, I think it would be advisable to look at wikipedia's page and think about what kind of new stuff you can offer than what is already there. If not, then I think you should take on a new project that is not explored very much.
Leah 19:35, 24 June 2011 (UTC)Although this is a physic topic, I just want to make sure it's capable of being a math image page.

• Kate 16:39, 6 July 2011 (UTC): Snell's Law is a mathematical formula that predicts the amount of bend. - amount of bend in what? Feels like the sentence stopped before it was over.
Ljeanlo1 23:56, 6 July 2011 (UTC) Would it be better if I end off with "seen in the image"?
Yeah, I think that'd be fine. Or you could say that it predicts the amount that light bends. You just need to tie the bending down somewhere, because it's not like Snell's Law is predicting the amount that like, a tree branch or a river or my left pinky finger bends. (Kate 14:51, 7 July 2011 (UTC))

Ljeanlo1 15:51, 13 July 2011 (UTC) Ok, got it.

## Basic Description

Kate 16:39, 6 July 2011 (UTC):

• Geometrical optics will requires basic knowledge of geometry specifically on triangles.
I think this sentence should be "Understanding geometrical optics requires basic knowledge of geometry and triangles."
Ljeanlo1 23:56, 6 July 2011 (UTC) Changed the sentence.
• In contrast, light can sometimes be treated as a wave which is found in physical optics, but that involves the interference and propagation of waves which will require more insight into physics.
Even though you follow it by saying that physical optics won't be discussed, this sentence is a little intimidating to read. You might want to see if you can find a less detailed way of saying that there's other ways of understanding light.

Ljeanlo1 16:07, 13 July 2011 (UTC)I have broken this up and wrote that it will not be discussed. I think it's important to add little snippets of other topics in case anyone would like to learn about physical optics on a quick wiki search. Also, I took out the concept of physical optics and just said that light sometimes behaves in a different way.

Gene 19:13, 24 June 2011 (UTC) "geometrical optics where it's known that light travels in a straight line called a ray"--but you're talking about when it doesn't!

• Rebecca 01:45, 7 July 2011 (UTC) "Physical optics will not be discussed...." I would add "on this page."

Ljeanlo1 16:07, 13 July 2011 (UTC) I included this.

### Law of Reflection

Kate 16:39, 6 July 2011 (UTC):

• The incident ray makes with the normal an angle of incidence.
The wording here confused me, it might sound better to say "The angle that the incident ray makes with the normal is called the angle of incidence."
Ljeanlo1 23:56, 6 July 2011 (UTC) Changed the sentence.
• I need a bit more explanation for why Image 3 shows distortion and Image 2 doesn't - to me, they both look like they're essentially the same thing as Image 1 - there's multiple light rays in each picture, and each ray follows the law of reflection. Is the point that in Image 2 the light rays enter and exit in parallel with each other? If so, shouldn't the light rays in Image 3 enter in parallel and then exit in different directions? (Right now, the rays in Image 3 look totally unrelated to each other to me.)

*Rebecca 01:46, 7 July 2011 (UTC) "The reflected ray holds the same property of making an angle of reflection with the normal." I'm not sure if you need this sentence because if it reflects it seems sort of obvious that it would make an angle.

• Bolding new words that you're defining really helps in this section.
• Rebecca 01:14, 16 July 2011 (UTC) This section is great now. I think it's very clear. Only one question: is this actually a law of reflection? If so, what is the law specifically? If you can identify a law in here I think that would be helpful. Otherwise, I think the section would be more appropriately named "Reflection of Light" or something like that.

Ljeanlo1 15:04, 18 July 2011 (UTC) It's not a law really but I'll take your suggestion by renaming the title.

### Refraction

Kate 16:39, 6 July 2011 (UTC):

• It is 3.0 x 10^8 m/s - you should probably make that 8 an actual super script. I don't know how to type the html so that you can see the code, but I guess you can just look at this under edit - it should look like this: 108
• When you're typing "c" and "v" and "n", do you mean c and v and n?
Ljeanlo1 23:56, 6 July 2011 (UTC) I'll put it in italics instead of quote marks.
I mean, you don't have to. That's just how I would do it, and I know a lot of the time I mess up quotation marks with two single quotes and don't get italics where I want them, so I thought I'd ask.(Kate 14:55, 7 July 2011 (UTC))

Ljeanlo1 16:41, 13 July 2011 (UTC)No, it's ok. I think I should be consistent.

*such as air and carbon dioxide, have an index of refractive - should that be "index of refraction"? I don't know the terminology, but that's what you called it when you bolded it.

• The beginning of this section (explaining that light travels at different speeds in different materials) was good, and the ending seemed clear too (explaining different refractive indices and connecting them to the diagram), but I think you need to be more explicit in the middle about how light changing speeds changes the angle of the ray. I think I kind of remember it from physics, but if you want to write the basic description for someone who knows no physics, you're going to have to spell it out.

Ljeanlo1 16:41, 13 July 2011 (UTC) I added some more text to this section. I don't know if it's clear enough so have a look.

• "It is $3.0 x 10^8 \mathrm{m}/\mathrm{s}$" ?

xd 14:23, 22 June 2011 (UTC) I think you mean $3.0 \times 10^8 \mathrm{m}/\mathrm{s}$

• Leah 19:32, 24 June 2011 (UTC) I fixed this.

Gene 19:13, 24 June 2011 (UTC) The speed of light differs when it travels through a certain medium" -- you mean ANOTHER medium, I bet. "index of refractive,"n""-- don't you mean "index of REFRACTION?

• Leah 19:32, 24 June 2011 (UTC) Sorry. I fixed these grammatical errors.

"The ratio of the speed of light in a vacuum, "c", and the speed of light in a medium, "v", is the index of refraction , "n"" -- it would help some of us if you wrote n = c/v.

• Leah 19:32, 24 June 2011 (UTC) I have included the mathematical representation of the description.

Generally, clear writing.

### Definition

Kate 16:39, 6 July 2011 (UTC):

• Snell's law relates the angle of incidence and refraction along with the index of refraction for media.
I don't really understand this sentence. I don't know what you mean by "media", and I think maybe you mean "angles" because there's two of them? And I find the sentence structure "X relates Y and Z along with W" a little confusing. Something like "X gives the relationship between Y, Z, and W" or "X relates Y and Z to W" would be clearer, I think.

Ljeanlo1 17:16, 13 July 2011 (UTC) I have rearranged the sentence.

• I'd really like for there to be some sort of words version of the law after you give the equation. What does the equation mean? Just that the amount of refraction is dependent upon the indices of refraction?

Ljeanlo1 17:16, 13 July 2011 (UTC)I've added a word explanation of the Law at the beginning. Tell me what you think about it.

## A More Mathematical Explanation

*Kate 17:05, 6 July 2011 (UTC): Below give two methods in deriving Snell's Law, additional information, and problems that you can solve.

This sentence doesn't mean what you want it to mean. Try "Given below are two methods…"

### Deriving Snell's Law with Refraction

Kate 17:05, 6 July 2011 (UTC):

• I don't think you should just call it "Snell" in the subject heading here, it should be "Snell's Law"

*Typo: Speed is based on how much distance is traveled in an amount of time.

• You're missing punctuation between the sentence that begins "The wavelength in a medium…" and the one that begins "It was mentioned…"

*Equate for the common hypotenuse gives:

First, the equation after this isn't showing up. Second, I think maybe you mean "Solving for" and not "Equate"?
• Are you sure your math in this section is right? In the last equation, n1 and n2 are on the same side as the thetas with the same index, but in the equation before that, they're still on the sides with the matching thetas, but are in the denominator. I don't know if I explained that well - what I'm trying to say is that it looks to me like you simplified $\frac{1}{n} \sin(\theta)$ to $n \sin(\theta)$.

Ljeanlo1 17:37, 13 July 2011 (UTC) Do you think it's best that I put parentheses around theta. I don't really do that when I'm writing out my math on a piece of paper even though I know it's suppose to be there?

Ljeanlo1 17:27, 13 July 2011 (UTC)I have changed the syntax of the math so that the steps looks more clear.

*Rebecca 01:47, 7 July 2011 (UTC) I would bold "period" when you define it.

### Total Internal Refraction

Kate 17:16, 6 July 2011 (UTC):

• I don't understand your first paragraph in this section. I think it's a combination of confusing wording and me having a hard time visualizing what you're talking about.
• I don't think you really mean to write "sin1", but I don't know what you actually are trying to say.
• I guess I really just don't understand this section. I don't know what the purpose of it is - I thought you said we were going to do two derivations of Snell's Law, but this doesn't look like a derivation. It'll probably help when you get your pictures in there, but it might be a good idea to go over the text with someone who understands the physics and try and make it clearer.

Ljeanlo1 15:07, 18 July 2011 (UTC)

I moved everything to the why it's interesting part and I tried to be as clear as possible. Take a look again.

### Snell Law's on the Beach

• Kate 17:18, 6 July 2011 (UTC): I think the lifeguard example is a good one, but if you're using it just to begin the derivation, you should make that clearer at the start - I thought we were doing an example problem, but then when I saw the next heading, I was like, "huh? why is there a derivation here??"

• Rebecca 01:48, 7 July 2011 (UTC) Lifeguard is one word.
• I think your diagram for the beach problem is helpful, but your black and red lines for "path with the least water" and "path with the least sand" aren't exactly true. For example, the black line shows just one choice of path with the least water. You could also run directly to the point where the T in "path with the least time" intersects the black line, and then run to the water and you'd still spend the same amount of time in the water. I'm not sure if there's a way to change this, and if not, don't worry too much. Just figured I'd point it out and maybe some of the other imagers have ideas.

Ljeanlo1 23:49, 13 July 2011 (UTC) I see what you mean, but I thought I would outlined the most common option a person would have if they were to point how the path with the least ____ (insert word). I'll ask other people what they think about it.

#### Deriving Snell With Fermat

• Kate 17:18, 6 July 2011 (UTC): I found it kind of weird the way you said that it's usually "required" in middle school that you know d = rt. I think perhaps it would be better just to say "Recall that distance equals rate multiplied by time"

Ljeanlo1 18:00, 13 July 2011 (UTC) I took this sentence out and put in what you suggested.

• Rebecca 01:48, 7 July 2011 (UTC) "Usually in middle school, it's required that everyone know distance is equal to the rate times time (d=rt)." I would remove this sentence. I think it might intimidate people if they didn't learn this in middle school or they forgot it, and you don't really need it. Maybe also remove "Velocity is easy though." I think it's the same idea- if people don't immediately understand they will get discouraged.

Ljeanlo1 18:00, 13 July 2011 (UTC)I took out both of these sentences and said to rename rate as velocity.

• Rebecca 01:18, 16 July 2011 (UTC) I think you accidentally left "Velocity though is easy."
• When you say "So the total time from point A to point B is..." I think you need another sentence of explanation. Maybe try... "Using plugging these formulas for distance into the equation for time, we can find the total time from point A to point B. It is:"

Ljeanlo1 18:00, 13 July 2011 (UTC) Thanks. I used your sentence which was very clear.

• I don't think you're really crossing out the 1/2 in the next line... you're multiplying both sides by 2 to make the 1/2 disappear. To show this I think you need to add an extra step. Also, you proceed to say that the two expressions are the same.... but it's not that easy to see. You'll have to reduce it more to show that they're actually the same.

Ljeanlo1 18:00, 13 July 2011 (UTC) I made it into more steps and included your suggestions about 2 vs. 1/2.

## Why It's Interesting

• Kate 17:20, 6 July 2011 (UTC): I thought the mirages were definitely a reason why it's interesting! I didn't know that at all.
• Rebecca 01:49, 7 July 2011 (UTC) I can't wait to see the new Why It's Interesting section and the applet! Nice work on this page.

Ljeanlo1 18:05, 13 July 2011 (UTC) I decided to put the total internal reflection part in this section, which I am revising. I plan to talk about fiber optic cables. Also, I want to expand on mirages if I can find a credible source. Lastly, people from Drexel suggest I do a section on ray tracing (this usually has to do with real/virtual images and what the eye sees.)