Verified Solution • 2025–26 Session moderate

QJEEM22Phe5ac: JEE Main 2022 Physics - Class 12 JEEM22Phe5ac Solution: Consider a light ray travelling in air is incident into a…

Consider a light ray travelling in air is incident into a medium of refractive index 2n\sqrt{2n} . The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

Multiple Choice Options

  • A sin⁡−1(n){\sin ^{ - 1}}\left( {\sqrt n } \right)
  • B cos⁡−1(n2){\cos ^{ - 1}}\left( {\sqrt {{n \over 2}} } \right)
  • C sin⁡−1(2n){\sin ^{ - 1}}\left( {\sqrt {2n} } \right)
  • D 2cos⁡−1(n2)2{\cos ^{ - 1}}\left( {\sqrt {{n \over 2}} } \right)

Step-by-Step Verified Solution

According to the law,

1×sin⁡θ=2n×sin⁡(θ2)1 \times \sin \theta = \sqrt {2n} \times \sin \left( {{\theta \over 2}} \right)

⇒cos⁡θ2=n2\Rightarrow \cos {\theta \over 2} = \sqrt {{n \over 2}}

⇒θ=2cos⁡−1(n2)\Rightarrow \theta = 2{\cos ^{ - 1}}\left( {\sqrt {{n \over 2}} } \right)

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