Simple proof of Snell's law without calculus

Click For Summary

Discussion Overview

The discussion revolves around the possibility of proving Snell's law without the use of calculus. Participants explore various approaches, including Fermat's principle, and debate the necessity of calculus in deriving the law.

Discussion Character

  • Debate/contested
  • Exploratory
  • Technical explanation

Main Points Raised

  • Some participants express a desire to find a proof of Snell's law that does not involve calculus, referencing Fermat's principle as a potential method.
  • Others argue that Fermat's principle is inherently linked to calculus, as it involves variational principles and the concept of least time.
  • A participant claims to have seen a proof by R.P. Feynman that does not use calculus, although this claim is contested by others who assert that Feynman's example is not a true proof.
  • One participant suggests using the isotropy of space and time invariance of physical law, although they note this may only apply to total reflection.
  • Another participant proposes that matching wavevectors parallel to the surface does not require calculus, relying instead on vector arithmetic.
  • A historical perspective is introduced, noting that Fermat's principle predates calculus, suggesting he may have approached the problem differently.
  • Reference is made to H.C. Verma's work, which purportedly contains a simple proof of Snell's law.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether Snell's law can be proven without calculus. Multiple competing views are presented, with some insisting that calculus is essential while others believe alternative methods exist.

Contextual Notes

The discussion reflects varying interpretations of Fermat's principle and its relation to calculus, as well as differing opinions on the validity of proofs presented by Feynman and others. The historical context of Fermat's work is also noted, highlighting potential limitations in understanding his original methods.

shihab-kol
Messages
119
Reaction score
8
Well, I have checked out the ones with calculus but I was just wondering if there was one without calculus
I tried it but could not do it
I think Fermat's principle can be used to do it but I am not being successful
So, anyone please help
 
Science news on Phys.org
shihab-kol said:
I think Fermat's principle can be used to do it but I am not being successful
Yes. I've found it on Wikipedia, but I do not know what you mean by "without calculus". I even don't know, how to formulate it without calculus.
 
shihab-kol said:
I think Fermat's principle can be used to do it but I am not being successful

No surprise since Fermat's principle is a type of variational principle, so it is somewhat connected to calculus.
 
shihab-kol said:
Well, I have checked out the ones with calculus but I was just wondering if there was one without calculus
I tried it but could not do it
I think Fermat's principle can be used to do it but I am not being successful
So, anyone please help

This question doesn't make any sense. It is like asking if one can do kinematics with something that has variable velocity and acceleration but without calculus. In many of these cases, not using calculus is NOT an option!

And as stated already, Fermat Principle itself is based on calculus, i.e. finding the path of least time, which is a variational calculus application (see Pg. 8 of this document). So I have no idea why you'd think that using Fermat Principle is not using calculus.

Zz.
 
ZapperZ said:
This question doesn't make any sense.

Zz.

Oh yes it does.
And as stated already, Fermat Principle itself is based on calculus, i.e. finding the path of least time, which is a variational calculus application (see Pg. 8 of this document). So I have no idea why you'd think that using Fermat Principle is not using calculus.

But it can be done WITHOUT calculus too.

You can prove snell's law too WITHOUT calculus.

I have seen the proof and it is by R.P.Feynman.
So, thanks but no thanks
 
shihab-kol said:
I have seen the proof and it is by R.P.Feynman.

Feynman's "proof" isn't really a proof. At least the example I've seen from his lectures isn't. It explains how you can use geometry to find an answer in a specific case where there's a single boundary and two non-varying refractive indices. A real proof inherently requires calculus because it has to deal with continuously varying variables. Page 8 in Zz's link contains this exact situation and you cannot use geometry by itself to solve it.
 
  • Like
Likes   Reactions: weirdoguy
Can't you use the property of isotropy of space and the time invariance of physical law? But that may only prove that incident angle is equal to the reflected angle for total reflection.
 
shihab-kol said:
Oh yes it does.But it can be done WITHOUT calculus too.

You can prove snell's law too WITHOUT calculus.

I have seen the proof and it is by R.P.Feynman.
So, thanks but no thanks

since you are going against good advice and say it can be done
then the onus is on you to show us how it is done and we can see if it makes sense
 
You only have to match the wavevectors parallel to the surface of the light inside and outside the medium. This doesn't involve calculus, merely vector arithmetics.
 
  • #10
But when fermat devised his principle at that time there was no calculus. As calculus came much after by Newton and leibnitz.Fermat must have done in his own way.Or he just gave us an intuitional principle with no proof or he had find maxima or minima in his own way.

I gues this question/topic needs importance.

http://aapt.scitation.org/doi/10.1119/1.1514235

Moderator's edit: File substituted by link due to potential copyright violation.
 
Last edited by a moderator:
  • #11
Thanks.
Being an Indian,perhaps you have gone through H.C.Verma .There also you will find a simple but elegant proof of the above.
I did not post anything since by the time I started the thread the book has been returned and I could not include the proof on the site .
Thanks once again.
 

Similar threads

High School Fermat's principle and refraction -- Possible misunderstanding
  • · Replies 42 ·
2
Replies
42
Views
5K
Undergrad Snell's law from a mechanical model
  • · Replies 12 ·
Replies
12
Views
3K
Graduate How to compute phase gradient from Snell's law?
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Understanding a Generalization of Snell's Law
  • · Replies 19 ·
Replies
19
Views
6K
Graduate Infinitesimal, Snell's law, and ray tracing
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Birefringence in in uniaxial optical media and Snell's law
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Fermat's Principle, Snell's Law, and the Prism
  • · Replies 8 ·
Replies
8
Views
3K
Graduate Fermat & Snell: Solving the Derivation Mystery
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Does Fermat's principle ever give the longest time?
  • · Replies 20 ·
Replies
20
Views
5K
Graduate Proof of Fermat and Huygens–Fresnel principle
  • · Replies 1 ·
Replies
1
Views
3K