Snell's Law: From n sin theta to n1sintheta1 = n2sintheta2

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SUMMARY

Snell's Law is expressed in two forms: n1sin(theta1) = n2sin(theta2) and n sin(theta) = constant. The latter arises from the principle that when light transitions between different media, the product of the refractive index (n) and the sine of the angle of incidence (theta) remains constant. This constancy occurs because the refractive indices of the media differ, yet the relationship between them maintains a fixed value during the transition of light. Understanding this relationship clarifies the behavior of light as it refracts through various materials.

PREREQUISITES
  • Understanding of Snell's Law and its mathematical formulation
  • Basic knowledge of refractive indices of different media
  • Familiarity with the concept of light refraction
  • Mathematical skills to manipulate trigonometric equations
NEXT STEPS
  • Study the derivation of Snell's Law from wave optics principles
  • Explore the implications of refractive indices in different materials
  • Learn about the applications of Snell's Law in optical devices
  • Investigate the relationship between light speed and refractive index
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Students of physics, optical engineers, and anyone interested in the principles of light behavior and refraction in different media.

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Hi, I'm new to the forum as I'm struggling to find answers with an internet search.

I've seen Snell's Law stated as n sin theta = constant.

How does this arise from its more familiar form of n1sintheta1 = n2sintheta2? I can't work it out.

Thanks for reading!
 
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Well, that's in fact something very straight forward and has no intermediate mathematical steps. Its just that when something is not changing while time goes on, then its constant. So when light is moving between different media and , although different media have different refraction indices and the light experiences different angles of refraction, it will always have the same n \sin\theta. So this quantity doesn't change, so its a constant!
 

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