Maths and Physics (Example: Refraction of Light)

“Physics without maths is like trying to drive a car without fuel”

-reddit comment (xsnac)

Mathematics is believed to be the language of physics. If you are into physics, mathematics is inevitable. Mathematics concerns itself with abstract ideas. And physicists use those abstract relationships to replace it with the physical things and get the quantitative relationship. And sometime, physicists demand a new tool to solve its problems and mathematics creates it for them.

In order to taste the flavor of mathematics and understand the affair between its concept and that of physics, one must try to think of some physical example that could fit in perfectly with that mathematical concept. For example, I used to have a problem with discontinuous functions. My maths teacher used to write three different relations for the same variable, and I used to think, where I would find something like this. Something behaves in certain way up to some point and then decides to change its behavior? So I tried to think of some example in the physical world which behaves in this weird fashion, and lo and behold, we have refraction.

The Example

Consider the figure…

Physics and Maths 2

A light ray originates from the optically denser medium, crosses the interface and enters the rarer medium. In this example I have considered the denser medium to be glass, with refractive index 1.5, and rarer medium to be air, with refractive index of about 1. As the light ray crosses the interface, the ray gets bent away from the normal. I have considered two angles θ1 and θ2 and I have to find the relationship between them.

The Relation

Physics and Maths 3

So we have three different relationships to form one function of θ2. Up to the critical angle (approximately 41.80 for Glass-Air interface), the relationship between them can be found by manipulating Snell’s Law of refraction. But after critical angle, the relationship suddenly changes as Total Internal Reflection (TIR) begins. The relationship becomes linear as per the law of reflection. This relationship holds until θ1 becomes a right angle after which it once again follows Snell’s law but with incident ray in the rarer medium.

The Graph

The graph of this can be plotted as below. I could have used excel to plot but I wanted to kill a little more time so I plotted manually.

Physics and Maths 1

 

And finally we have some physical example for the abstract mathematical concept. I don’t know whether, this concept was derived because of some physical observation or the mathematical concept came first, but I was really happy that I could relate it. If you find any other physical example please share with me. Till then, thanks for reading.

 

References:

  1. For Total Internal Reflection: https://en.wikipedia.org/wiki/Total_internal_reflection (Or any fundamental physics textbook)
  2. For the opening quote: https://www.reddit.com/r/AskPhysics/comments/44tol0/good_lectures_or_books_on_hydrostatics_without/

43 Comments

  1. Undeniably believe that which you stated. Your favorite reason seemed to be on the web the easiest thing to be aware of. I say to you, I definitely get annoyed while people think about worries that they just don’t know about. You managed to hit the nail upon the top and also defined out the whole thing without having side effect , people could take a signal. Will likely be back to get more. Thanks

  2. whoah this blog is wonderful i love reading your articles. Keep up the good work! You know, lots of people are looking around for this info, you can help them greatly.

  3. I like what you guys are often up too. This particular
    clever work and exposure! Continue the amazing works guys I’ve added you guys to my own, personal blogroll.

  4. It’s a shame you don’t have a donate button! I’d undoubtedly donate
    to this particular outstanding blog! I suppose for the present time i’ll settle for
    book-marking and adding your RSS feed to my Google account.
    I look ahead to new updates and can speak about this blog with
    my Facebook group. Talk soon!

    • Hey thanks for the appreciation, it means a lot. We had not expected this level of response. We would like to get more professional before we could ask anyone to contribute. We will be adding it once we feel comfortable enough to accept it, till then we are focussed on creating good content for our awesome followers. Thank you very much for your response. 🙂

  5. I simply want to say I am just beginner to blogging and absolutely liked your blog. More than likely I’m likely to bookmark your website . You amazingly have superb articles and reviews. Cheers for sharing your blog.

  6. Wow! This web site looks exactly like my old one! It’s with a entirely different subject but it really has virtually a
    similar layout and design. Great selection of
    colors!

  7. My partner and so i stumbled right here different website and thought I might check things out.

    I really like what I see so now i am following you.
    Enjoy looking over your web page again.

  8. I simply want to say I am all new to blogs and absolutely enjoyed this web-site. Most likely I’m going to bookmark your blog . You actually have fantastic well written articles. Regards for sharing with us your website page.

  9. I simply want to mention I’m very new to blogging and site-building and seriously loved you’re blog. More than likely I’m going to bookmark your blog . You amazingly come with fantastic writings. With thanks for revealing your web page.

  10. I simply want to tell you that I am just very new to blogging and seriously liked you’re web blog. Almost certainly I’m planning to bookmark your site . You amazingly have outstanding articles and reviews. Many thanks for revealing your website.

  11. I want to to thank you for this fantastic read!! I definitely loved every little
    bit of it. I have you book-marked to look at new things
    you post…

  12. We are a group of volunteers and opening a new scheme in our community.
    Your web site offered us with helpful info to work on.
    You’ve performed an impressive task and our whole neighborhood will be thankful to you.

  13. Hello! Do you use Twitter? I’d like to follow you if that would be
    okay. I’m absolutely enjoying your blog and look forward to new updates.

  14. You can definitely see your enthusiasm in the article you write.
    The world hopes for more passionate writers like you who
    aren’t afraid to say how they believe. All the time follow
    your heart.

  15. Thank you a bunch for sharing this with all folks you actually know what you’re speaking
    approximately! Bookmarked. Please also seek advice from my site =).
    We will have a hyperlink alternate agreement between us

  16. Sweet blog! I found it while browsing on Yahoo News.
    Do you have any suggestions on how to get listed in Yahoo News?
    I’ve been trying for a while but I never seem to get
    there! Appreciate it

  17. I think this is one of the most important info for me.
    And i’m glad reading your article. But should remark on some general things, The website style is perfect, the articles
    is really excellent : D. Good job, cheers

  18. Wow, incredible weblog structure! How lengthy
    have you ever been blogging for? you make running a blog
    glance easy. The total look of your site is wonderful,
    as neatly as the content!

  19. I added a new blog post yesterday. There’s a smaller list than usual in it.
    I’m currently working on a bigger list.
    It’s going to take some time to compile it. I hope all of you are
    having a good week. I’m planning on doing some design changes to my site.

    I’m also thinking about adding some new things too. I’ll talk
    more about that in the days and weeks to come.

  20. I actually wanted to type a brief remark so as to appreciate you for all the superb tips and hints you are writing at this site. My incredibly long internet investigation has at the end of the day been compensated with professional know-how to exchange with my neighbours. I would assert that most of us site visitors are very much endowed to exist in a fine site with many special professionals with useful tips and hints. I feel very much blessed to have seen the site and look forward to tons of more cool minutes reading here. Thanks a lot again for everything.

  21. I actually wanted to type a small message to be able to say thanks to you for all of the marvelous ideas you are writing at this website. My time consuming internet lookup has now been recognized with reasonable information to write about with my partners. I would claim that we readers are extremely fortunate to exist in a remarkable site with very many wonderful individuals with insightful plans. I feel rather blessed to have discovered your entire site and look forward to some more fun minutes reading here. Thanks a lot once again for everything.

  22. I want to express my appreciation for your kind-heartedness for men and women who need assistance with this one subject matter. Your personal commitment to passing the message across turned out to be rather insightful and has without exception helped associates like me to reach their pursuits. Your entire useful help and advice entails a whole lot to me and still more to my peers. Warm regards; from everyone of us.

  23. Thank you for the good writeup. It in fact was a amusement account it.
    Look advanced to more added agreeable from you! By the way, how could we communicate?

  24. Thank you a lot for sharing this with all folks you really recognise what you are speaking approximately!
    Bookmarked. Please also talk over with my website =).
    We can have a hyperlink alternate arrangement among us

  25. I am also writing to let you know of the incredible experience my girl encountered studying your web site. She noticed lots of pieces, most notably what it is like to have a marvelous helping style to get other people with ease understand certain hard to do matters. You truly surpassed our own expected results. Thank you for providing those informative, trusted, edifying not to mention cool guidance on this topic to Janet.

  26. I would like to point out my admiration for your kind-heartedness in support of men and women who really need guidance on this one concept. Your personal dedication to passing the message all through became incredibly valuable and have without exception allowed somebody much like me to achieve their targets. Your new interesting recommendations entails this much to me and much more to my office colleagues. Warm regards; from each one of us.

Leave a Reply

Your email address will not be published.


*