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Wave Optics

Question
CBSEENPH12039548

Let the xz-plane be the boundary between two transparent media. Medium 1 in z ≥ 0 has a refractive index of √2 and medium 2 with z<0 has a refractive index of √3. A ray of light in medium 1 given by the vectorstraight A space equals space 6 square root of 3 space bold i with bold hat on top bold space bold plus bold space 8 square root of 3 space bold j with bold hat on top minus 10 bold k with hat on top is incident on the plane of separation. The angle of refraction in medium 2 is

  • 45° 

  • 60° 

  • 75° 

  • 30° 

Solution

A.

45° 

As a refractive index for z>0 and z≤0 is different xy-plane should be the boundary between two media.
Angle of incidence,
space cos space straight i space space equals space open vertical bar fraction numerator straight A subscript straight z over denominator square root of straight A subscript straight x superscript 2 space plus straight A subscript straight y superscript 2 plus straight A subscript straight z superscript 2 end root end fraction close vertical bar space equals 1 half
straight i space equals space 60 to the power of straight o
From space Snell apostrophe straight s space law comma space fraction numerator sin space straight i over denominator sin space straight r end fraction space equals space straight mu subscript 2 over straight u subscript 1 space equals space fraction numerator square root of 3 over denominator square root of 2 end fraction
sin space straight r space equals space fraction numerator square root of 3 space end root space straight x space square root of 2 over denominator square root of 3 space straight x 2 end root end fraction rightwards double arrow space straight r space space equals space 45 to the power of straight o

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