Finding the Critical Angle for T.I.R.

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SUMMARY

The critical angle for total internal reflection at an air-material interface, given Brewster's angle of 63°, is determined to be 31°. The refractive index of air (n1) is 1.000, and the refractive index of the material (n2) is calculated to be 1.963 using the formula tan(63°) = n2/n1. The critical angle (θc) is then found using the equation sin(θc) = n1/n2.

PREREQUISITES
  • Understanding of Snell's Law
  • Familiarity with refractive indices
  • Knowledge of Brewster's angle
  • Basic trigonometry
NEXT STEPS
  • Study the derivation of Snell's Law
  • Explore applications of Brewster's angle in optics
  • Learn about total internal reflection in fiber optics
  • Investigate the relationship between refractive index and wavelength
USEFUL FOR

Students studying optics, physics educators, and professionals in optical engineering will benefit from this discussion on critical angles and total internal reflection.

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Homework Statement



When light strikes an air-material interface from the air side, Brewster’s angle is 63°.
What is the critical angle for total internal reflection for light striking the interface from
the material side?


Homework Equations



tanθB=n2/n1

sinθc=n1/n2
(n2 is greater than n1)

The Attempt at a Solution



n1=1.000

tan63=n2/1.000

n2=1.963

sinθc=(1.000/1.963)

θc=31°
 
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It is correct.

ehild
 

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