JEE Main 2015 — Physics Optics

2015mcqmedium

Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is $\mu$ , a ray, incident at an angle $\theta$ , on the face AB would get transmitted through the face AC of the prism provided:

JEE Main 2015 Physics, Ray Optics — question figure

Official previous-year question

Held on 4 Apr 2015 · Verified 6 Jul 2026.

Options

A
$\theta < {\text{cos}}^{ - 1 } [ \mu sin ( \text{A} + {\text{sin}}^{ - 1 } ( \frac{ 1 }{ \mu } ) ) ]$
B
$\theta >{\mathrm{sin}}^{-1}[\mu sin(A-{\mathrm{sin}}^{-1}(\frac{1}{\mu }))]$
C
$\theta < {\text{sin}}^{ - 1 } [ \mu sin ( \text{A} - {\text{sin}}^{ - 1 } ( \frac{ 1 }{ \mu } ) ) ]$
D
$\theta >{\mathrm{cos}}^{-1}[\mu sin(A+{\mathrm{sin}}^{-1}(\frac{1}{\mu }))]$

Did you get this right?

Solution

Central Idea: The ray will get transmitted through face $AC$ if ${i}_{AC}<{i}_{C}$

Consider the ray diagram is shown below.

JEE Main 2015 Physics, Ray Optics — solution figure

A ray of light incident on face $AB$ at an angle $\theta$

${r}_{1}=$ Angle of refraction on face $AB$

${r}_{2}=$ Angle of incidence at face $AC$

For transmission of light through face $AC$

${i}_{AC}<{i}_{C}$

or $A-{r}_{1}<{i}_{C}$

or $\mathrm{sin}(A-{r}_{1})<\mathrm{sin}{i}_{C}$

or $\mathrm{sin}(A-{r}_{1})<\frac{1}{\mu }$

$A-{r}_{1}<{\mathrm{sin}}^{-1}(\frac{1}{\mu })$

or $\mathrm{sin}{r}_{1}>\mathrm{sin}[A-{\mathrm{sin}}^{-1}(\frac{1}{\mu })]$

Now, applying Snell's law at the face $AB$

$1\times \mathrm{sin}\theta =\mu \mathrm{sin}{r}_{1}$

or $\mathrm{sin}{r}_{1}=\frac{\mathrm{sin}\theta }{\mu }$

$\Rightarrow \frac{\mathrm{sin}\theta }{\mu }>\mathrm{sin}[A-{\mathrm{sin}}^{-1}(\frac{1}{\mu })]$

or $\theta >{\mathrm{sin}}^{-1}[\mu \mathrm{sin}{A-{\mathrm{sin}}^{-1}(\frac{1}{\mu })}]$

Your note

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Options

$\theta < {\text{cos}}^{ - 1 } [ \mu sin ( \text{A} + {\text{sin}}^{ - 1 } ( \frac{ 1 }{ \mu } ) ) ]$

$\theta >{\mathrm{sin}}^{-1}[\mu sin(A-{\mathrm{sin}}^{-1}(\frac{1}{\mu }))]$

$\theta < {\text{sin}}^{ - 1 } [ \mu sin ( \text{A} - {\text{sin}}^{ - 1 } ( \frac{ 1 }{ \mu } ) ) ]$

$\theta >{\mathrm{cos}}^{-1}[\mu sin(A+{\mathrm{sin}}^{-1}(\frac{1}{\mu }))]$

Solution

Central Idea: The ray will get transmitted through face $AC$ if ${i}_{AC}<{i}_{C}$

Consider the ray diagram is shown below.

JEE Main 2015 Physics, Ray Optics — solution figure

A ray of light incident on face $AB$ at an angle $\theta$

${r}_{1}=$ Angle of refraction on face $AB$

${r}_{2}=$ Angle of incidence at face $AC$

For transmission of light through face $AC$

${i}_{AC}<{i}_{C}$

or $A-{r}_{1}<{i}_{C}$

or $\mathrm{sin}(A-{r}_{1})<\mathrm{sin}{i}_{C}$

or $\mathrm{sin}(A-{r}_{1})<\frac{1}{\mu }$

$A-{r}_{1}<{\mathrm{sin}}^{-1}(\frac{1}{\mu })$

or $\mathrm{sin}{r}_{1}>\mathrm{sin}[A-{\mathrm{sin}}^{-1}(\frac{1}{\mu })]$

Now, applying Snell's law at the face $AB$

$1\times \mathrm{sin}\theta =\mu \mathrm{sin}{r}_{1}$

or $\mathrm{sin}{r}_{1}=\frac{\mathrm{sin}\theta }{\mu }$

$\Rightarrow \frac{\mathrm{sin}\theta }{\mu }>\mathrm{sin}[A-{\mathrm{sin}}^{-1}(\frac{1}{\mu })]$

or $\theta >{\mathrm{sin}}^{-1}[\mu \mathrm{sin}{A-{\mathrm{sin}}^{-1}(\frac{1}{\mu })}]$

JEE Main 2015 — Physics Optics

Options

Did you get this right?

Solution

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JEE Main 2015 — Physics Optics

Options

Did you get this right?

Solution

Your note

JEE Main Optics in other years

More JEE Main Optics questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Thermodynamics

Waves & Oscillations

Keep practicing Optics