Critical Angle: Vacuum vs. Air Refraction

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SUMMARY

The discussion centers on the critical angle in optics, specifically addressing the formula for calculating it when light transitions from one medium to air or a vacuum. The formula for the critical angle is established as sin(critical angle) = n_2/n_1, where n_2 represents the index of refraction of the second medium, which is 1 for air or vacuum. The relationship is derived from Snell's law, n_1 sin(θ1) = n_2 sin(θ2, with the critical angle occurring when sin(θ2) equals 1.

PREREQUISITES
  • Understanding of Snell's Law in optics
  • Familiarity with the concept of the index of refraction
  • Basic knowledge of light behavior at medium boundaries
  • Ability to manipulate trigonometric functions
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  • Study the derivation and applications of Snell's Law in various media
  • Explore the implications of critical angle in fiber optics
  • Research the index of refraction values for different materials
  • Learn about total internal reflection and its applications
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Students of physics, optical engineers, and anyone interested in the principles of light behavior at the interface of different media.

Cheman
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Critical angle...

Is the formula:

sin(critical angle) = 1/ mu, only true light is moving from one medium into air/ a vacuum?

Thanks in advance. :smile:
 
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Correct. (Assuming "mu" is the index of refraction.) To generalize it to any two media (as long as [itex]n_2 < n_1[/itex]) go to Snell's law: [itex]n_1 \sin \theta_1 = n_2 \sin \theta_2[/itex]. The critical angle arises when [itex]\sin \theta_2 = 1[/itex], thus:
[tex]\sin \theta_{cr} = \frac {n_2}{n_1}[/tex]

When the second medium is air or vacuum, [itex]n_2 = 1[/itex].
 
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