- #1

shihab-kol

- 119

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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

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- Thread starter shihab-kol
- Start date

In summary, the book "H.C.Verma: A Comprehensive Treatise on Nonlinear Partial Differential Equations and Their Applications" has a simple but elegant proof of the above.

- #1

shihab-kol

- 119

- 8

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

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- #2

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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

- #3

weirdoguy

- 1,102

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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.

- #4

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shihab-kol said:

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.

- #5

shihab-kol

- 119

- 8

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

- #6

Drakkith

Mentor

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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.

- #7

Higgsono

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- #8

davenn

Science Advisor

Gold Member

2023 Award

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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

- #9

DrDu

Science Advisor

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- #10

Nikhil Kumawat

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.

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

shihab-kol

- 119

- 8

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.

Snell's law, also known as the law of refraction, is a fundamental law of physics that describes the relationship between the angles of incidence and refraction for a wave passing through a boundary between two different isotropic media.

A simple proof of Snell's law is important because it allows for a better understanding of the fundamental principles behind refraction and helps to build a strong foundation for further studies in optics and other related fields.

Yes, Snell's law can be proven using basic trigonometry and the principle of least time, which states that light will always take the path that requires the least amount of time to travel. This proof is often referred to as the "principle of least distance."

The key steps in a simple proof of Snell's law include defining the incident and refracted angles, applying the principle of least time, and using basic trigonometry to derive the relationship between the angles of incidence and refraction.

The simple proof of Snell's law is more accessible to those without a strong background in calculus, making it a more intuitive and easier to understand approach. However, the calculus-based proof provides a more rigorous and comprehensive understanding of the law and its applications.

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