Angle of Refraction: Prove Incident Beam is Parallel to Emerging Beam

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SUMMARY

The discussion confirms that for a light beam transitioning from medium 1 to medium 2, where medium 2 is a thick slab with an index of refraction n2, the emerging beam is parallel to the incident beam only when the incident angle is 0 degrees. This is established through the equation μ sin x = k, where for sin x1 = sin x2, the equality holds true only when n1 equals n2, which is not the case here. Therefore, the only scenario allowing for parallelism is when the light ray strikes the surface of medium 2 perpendicularly.

PREREQUISITES
  • Understanding of Snell's Law and refraction principles
  • Knowledge of indices of refraction (n1 and n2)
  • Familiarity with geometric optics concepts
  • Basic mathematical skills for manipulating trigonometric equations
NEXT STEPS
  • Study Snell's Law in detail to understand light refraction
  • Explore the concept of total internal reflection and its applications
  • Investigate the behavior of light in different mediums with varying indices of refraction
  • Learn about optical devices that utilize refraction, such as lenses and prisms
USEFUL FOR

Students of physics, optical engineers, and anyone interested in the principles of light behavior at material interfaces will benefit from this discussion.

Ronnin
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A light beam passes from medium 1 to medium 2 with the latter being a thick slab of material whose index of refraction is n2. Show that the emerging beam is parallel to incident beam.

Am I correct in assuming that the only way this is possible is to have the incident beam making an angle that is 90 degrees with medium 2? Can someone confirm my thinking.
 
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If there is only one refraction happening, then yeah. If there are two refractions (if its a slab or something so that the light ray emerges back into medium 1) then it will always be parallel to the incident ray.

Mathematically,

\mu sinx=k where k is a constant, so for sinx1=sinx2, n1=n2. Since n1 & n2 arent the same, the only angle for which the equality holds is 0, which means that the ray falls normally on surface 2.
 

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