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 the point $E$ on the face $BC.$ ![JEE Main 2019 Physics, Ray Optics — question figure](https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Ray_Optics/648b5a67417cc3fb48d66851/question_1__q_648b5a67417cc3fb48d66851__cdn-question-pool.getmarks.app__0459979_que__88f33f22a3_final_ppt_sync.jpg) Then, $\theta$ must satisfy

A transparent cube of side d, made of a… - JEE Main 2019 Physics PYQ

JEE Main 2019 — Physics Optics

2019mcqmedium

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 the point $E$ on the face $BC.$

JEE Main 2019 Physics, Ray Optics — question figure

Then, $\theta$ must satisfy

Official previous-year question

Held on 12 Apr 2019 · Verified 6 Jul 2026.

Options

A
$\theta <{\mathrm{sin}}^{-1}\sqrt{\frac{{\mu }_{2}^{2}}{{\mu }_{1}^{2}}-1}$
B
$\theta >{\mathrm{sin}}^{-1}\frac{{\mu }_{1}}{{\mu }_{2}}$
C
$\theta <{\mathrm{sin}}^{-1}\frac{{\mu }_{1}}{{\mu }_{2}}$
D
$\theta >{\mathrm{sin}}^{-1}\sqrt{\frac{{\mu }_{2}^{2}}{{\mu }_{1}^{2}}-1}$

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Solution

JEE Main 2019 Physics, Ray Optics — solution figure

At surface (1)

${\mu }_{1}\mathrm{sin}\theta ={\mu }_{2}\mathrm{sin}r \ldots (1)$

At surface (2)

${\mu }_{1}={\mu }_{2}\mathrm{sin}(90-r)$

${\mu }_{1}={\mu }_{2}\mathrm{cos}r...(2)$

From equation $(1)$ and $(2)$

$\Rightarrow \mathrm{sin}\theta =\frac{\mathrm{sin}r}{\mathrm{cos}r}$

$\Rightarrow \mathrm{sin}\theta =\frac{\frac{(\sqrt{{\mu }_{2}^{2}-{\mu }_{1}^{2}})}{{\mu }_{2}}}{(\frac{{\mu }_{1}}{{\mu }_{2}})}$

$\Rightarrow \mathrm{sin}\theta =\sqrt{\frac{{\mu }_{2}^{2}}{{\mu }_{1}^{2}}-1 }$

$\theta$ must satisfy,

$\Rightarrow \theta <{\mathrm{sin}}^{-1}(\sqrt{\frac{{\mu }_{2}^{2}}{{\mu }_{1}^{2}}-1})$

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