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QJEEM21Phbe7e: JEE Main 2021 Physics - Class 12 JEEM21Phbe7e Solution: A ray of light entering from air into a denser medium of…

A ray of light entering from air into a denser medium of refractive index 43{4 \over 3} , as shown in figure. The light ray suffers total internal reflection at the adjacent surface as shown. The maximum value of angle θ\theta should be equal to :

JEE Main 2021 (Online) 25th July Evening Shift Physics - Geometrical Optics Question 117 English

Multiple Choice Options

  • A sin⁡−173{\sin ^{ - 1}}{{\sqrt 7 } \over 3}
  • B sin⁡−154{\sin ^{ - 1}}{{\sqrt 5 } \over 4}
  • C sin⁡−174{\sin ^{ - 1}}{{\sqrt 7 } \over 4}
  • D sin⁡−153{\sin ^{ - 1}}{{\sqrt 5 } \over 3}

Step-by-Step Verified Solution

JEE Main 2021 (Online) 25th July Evening Shift Physics - Geometrical Optics Question 117 English Explanation 1

At maximum angle θ\theta ray at point B goes in gazing emergence, at all less values of θ\theta , TIR occurs.

At point B

43×sin⁡θ′′=1×sin⁡90∘{4 \over 3} \times \sin \theta '' = 1 \times \sin 90^\circ

θ′′=sin⁡−1(34)\theta '' = {\sin ^{ - 1}}\left( {{3 \over 4}} \right)

θ′=(π2−θ′′)\theta ' = \left( {{\pi \over 2} - \theta ''} \right)

At point A

1×sin⁡θ=43×sin⁡θ′1 \times \sin \theta = {4 \over 3} \times \sin \theta '

sin⁡θ=43×sin⁡(π2−θ′′)\sin \theta = {4 \over 3} \times \sin \left( {{\pi \over 2} - \theta ''} \right)

sin⁡θ=43cos⁡[cos⁡−174]\sin \theta = {4 \over 3}\cos \left[ {{{\cos }^{ - 1}}{{\sqrt 7 } \over 4}} \right]

JEE Main 2021 (Online) 25th July Evening Shift Physics - Geometrical Optics Question 117 English Explanation 2

sin⁡θ=43×74\sin \theta = {4 \over 3} \times {{\sqrt 7 } \over 4}

θ=sin⁡−1(73)\theta = {\sin ^{ - 1}}\left( {{{\sqrt 7 } \over 3}} \right)

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