A transparent cube of side d, made of a material of refractive index μ2, is immersed in a liquid of refractive index μ1(μ1 < μ2). A ray is incident on the face AB at an angle θ (shown in the figure). Total internal reflection takes place at point E on the face BC. The θ must satisfy

(A) \theta > {\sin ^{ - 1}}\,\frac{{{\mu _1}}}{{{\mu _2}}}

(B) \theta > {\sin ^{ - 1}}\,\sqrt {\frac{{\mu _2^2}}{{\mu _1^2}} - 1}

(C) \theta < {\sin ^{ - 1}}\,\frac{{{\mu _1}}}{{{\mu _2}}}

JEE Mains · Physics · STD 12 - Ray optics and optical instruments

A transparent cube of side \(d\), made of a material of refractive index \(\mu_2\), is immersed in a liquid of refractive index \(\mu_1(\mu_1 < \mu_2)\). A ray is incident on the face \(AB\) at an angle \(\theta \) (shown in the figure). Total internal reflection takes place at point \(E\) on the face \(BC\). The \(\theta\) must satisfy

Pick an option to check your answer.

Verified Solution

Correct Answer

(D) \(\theta < {\sin ^{ - 1}}\,\sqrt {\frac{{\mu _2^2}}{{\mu _1^2}} - 1} \)

Detailed explanation

\(\sin \mathrm{c}=\frac{\mu_{1}}{\mu_{2}}\)

\(\mu_{1} \sin \theta=\mu_{2} \sin \left(90^o-\mathrm{C}\right)\)

\(\sin \theta=\frac{\mu_{2} \sqrt{1-\frac{\mu_{1}^{2}}{\mu_{2}^{2}}}}{\mu_{1}}\)

\(\theta=\sin ^{-1} \sqrt{\frac{\mu_{1}^{2}-\mu_{2}^{2}}{\mu_{1}^{2}}}\)

For \(TIR\)

\(\theta<\sin ^{-1} \sqrt{\frac{\mathrm{u}_{2}^{2}}{\mu_{1}^{2}}-1}\)

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