(A) According to Brewster's law,the refractive index $n$ is given by $\tan \theta_{B} = n$,where $\theta_{B}$ is the Brewster angle.Given $\theta_{B}

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$\sin^{-1}\left(\frac{1}{\sqrt{6}}\right)$

(A) According to Brewster's law,the refractive index $n$ is given by $\tan \theta_{B} = n$,where $\theta_{B}$ is the Brewster angle.Given $\theta_{B} = 60^{\circ}$,we have $n = \tan 60^{\circ} = \sqrt{3}$.Now,using Snell's law,$\frac{\sin i}{\sin r} = n$,where $i = 45^{\circ}$ is the angle of incidence and $r$ is the angle of refraction.Substituting the values,$\sin r = \frac{\sin 45^{\circ}}{n} = \frac{1/\sqrt{2}}{\sqrt{3}} = \frac{1}{\sqrt{6}}$.Therefore,the angle of refraction is $r = \sin^{-1}\left(\frac{1}{\sqrt{6}}\right)$.

Class 12 Physics Ray Optics and Optical Instruments Refraction of Light

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$A$ beam of light is incident on a glass plate at an angle of $60^{\circ}$. The reflected ray is polarized. If the angle of incidence is $45^{\circ}$,then the angle of refraction is:

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A
$\sin^{-1}\left(\frac{1}{\sqrt{6}}\right)$
B
$\sin^{-1}\left(\frac{1}{\sqrt{3}}\right)$
C
$\sin^{-1}\left(\sqrt{\frac{3}{2}}\right)$
D
$\cos^{-1}\left(\sqrt{\frac{3}{2}}\right)$

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$(a)$ The refractive index of glass is $1.5$. What is the speed of light in glass? (Speed of light in vacuum is $3.0 \times 10^{8} \; m/s$).
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$A$ beam of light is incident on a glass plate at an angle of $60^{\circ}$. The reflected ray is polarized. If the angle of incidence is $45^{\circ}$,then the angle of refraction is:

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$(a)$ The refractive index of glass is $1.5$. What is the speed of light in glass? (Speed of light in vacuum is $3.0 \times 10^{8} \; m/s$).
$(b)$ Is the speed of light in glass independent of the colour of light? If not,which of the two colours,red or violet,travels slower in a glass prism?