Total Internal Reflection: Finding the angle?

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SUMMARY

The discussion focuses on calculating the angle of refraction for light entering an optical fiber with an index of refraction of 2.05 at an incidence angle of 51.0°. The critical angle was correctly calculated as 29.19 degrees using Snell's Law. However, the attempt to find the angle of refraction resulted in an incorrect answer of 22.27 degrees. The correct approach involves using Snell's Law accurately to determine the angle θ that the ray makes with the normal at the curved surface of the fiber.

PREREQUISITES
  • Understanding of Snell's Law and its application in optics
  • Knowledge of critical angle and total internal reflection
  • Familiarity with the concept of refraction in optical fibers
  • Basic trigonometry for angle calculations
NEXT STEPS
  • Review Snell's Law applications in optical systems
  • Study the concept of total internal reflection in detail
  • Explore the properties of light in different media
  • Practice problems involving critical angles and refraction
USEFUL FOR

Students studying optics, physics educators, and anyone interested in the principles of light behavior in optical fibers.

longcatislong
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Homework Statement



The figure below shows a ray of light entering one end of an optical fiber at an angle of incidence i = 51.0°. The index of refraction of the fiber is 2.05.

Diagram link: http://www.webassign.net/walker/26-55.gif

(a) Find the angle the ray makes with the normal when it reaches the curved surface of the fiber.

Homework Equations



Snell's Law: niSinThetai=ntSinThetat

The Attempt at a Solution



I found theta c (critical angle) to be 29.19 degrees, which correct as verified by my online homework. Then I tried answering part a using niSinThetai=NtSinThetat and got 22.27 degrees as my answer for part a). Online HW system says that's wrong.

Any help is much appreciated! Please tell me what I'm doing wrong and put me on the right track!
 
Physics news on Phys.org
22.27 degrees is the angle of refraction,θr. Determine θ.

ehild
 

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