Understanding Snell's Law and Maxwell's Equations with EM Waves

In summary, Snell's law is a principle in optics that describes the relationship between the angle of incidence and the angle of refraction when light passes through different mediums. It can be derived from Fermat's principle of least time or from Huygen's principle. Another approach is to solve Maxwell's equations with appropriate boundary conditions. This law is also related to the laws of reflection.
  • #1
3.14lwy
15
0
what is the snell's law?

and how to show this
n = sin(i)/sin(r)

(where
n = refractive index
i = angle of incident
r = angle of refraction )
??

thank you!
 
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  • #2
snell's law

You can derive snell's law from Fermat's principle of least time

www.physics.yorku.ca/undergrad_programme/highsch/SNELL3.html[/URL]

Another derivation can be done using Huygen's principle.



spacetime
[url]www.geocities.com/physics_all/index.html[/url]
 
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  • #3
Or you can just solve Maxwell's equations with appropriate boundary conditions.

Claude.
 
  • #4
Claude Bile said:
Or you can just solve Maxwell's equations with appropriate boundary conditions.

Claude.

Righto!

Maxwell's equations on EM Waves will provide the most elegent proof of Snells Law, Laws of Reflection and all the rest. You can read it from David Griffits "Intro ...to Electrodynamics".
 

1. How did Snell's law come about?

Snell's law was formulated by Dutch physicist Willebrord Snell in the 17th century. He observed that when light travels through different mediums, its direction changes. By conducting experiments, he discovered a relationship between the angle of incidence and the angle of refraction, which is now known as Snell's law.

2. What is Snell's law used for?

Snell's law is used to calculate the direction of light rays as they pass through different mediums, such as air, water, and glass. This is important in fields such as optics, astronomy, and engineering, where understanding the behavior of light is crucial.

3. How is Snell's law mathematically expressed?

Snell's law is mathematically expressed as n1sinθ1 = n2sinθ2, where n1 and n2 are the refractive indices of the two mediums, and θ1 and θ2 are the angles of incidence and refraction, respectively.

4. What are the applications of Snell's law?

Snell's law has various applications in everyday life, such as in the design of lenses for eyeglasses and cameras, as well as in the construction of optical instruments. It is also used in the study of atmospheric refraction, which affects how we see objects in the sky.

5. How does Snell's law relate to the speed of light?

Snell's law is closely related to the speed of light. The refractive index of a medium is a measure of how much the speed of light changes when it passes through that medium. The greater the difference in refractive indices between two mediums, the more the light will bend at the interface between them, as described by Snell's law.

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