Ray Optics

JEE Main level, single correct, medium

58 of 295

Question 58 of 295

A light wave travelling linearly in a medium of dielectric constant 44, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be :
(Given : relative permeability of medium μr=1{\mu }_{r}=1)

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Answer: (D) 60∘60^{\circ}

Relative refractive index is μ=μrϵr=4×1=2\mu =\sqrt{{\mu }_{r}{\epsilon }_{r}}=\sqrt{4\times 1}=2
Now, for complete reflection, θ>θc\theta \gt {\theta }_{c}, where, θc{\theta }_{c} is critical angle.
Now, critical angle is sin⁡θc=1μ=12\sin {\theta }_{c}=\dfrac{1}{\mu }=\dfrac{1}{2}
⇒θc=sin⁡−1(12)⇒θc=30∘\Rightarrow {\theta }_{c}={\sin }^{-1}\left(\dfrac{1}{2}\right) \Rightarrow {\theta }_{c}=30^{\circ}
So, the angle of incidence for which the total intensity of incident wave will be reflected back into the same medium is θ>30∘\theta \gt 30^{\circ} i.e., 60∘60^{\circ}.

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