JEE MAIN - Physics (2023 - 24th January Morning Shift - No. 3)
Given below are two statements :
Statement I : If the Brewster's angle for the light propagating from air to glass is $$\mathrm{\theta_B}$$, then the Brewster's angle for the light propagating from glass to air is $$\frac{\pi}{2}-\theta_B$$
Statement II : The Brewster's angle for the light propagating from glass to air is $${\tan ^{ - 1}}({\mu _\mathrm{g}})$$ where $$\mathrm{\mu_g}$$ is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below :
Both Statement I and Statement II are false
Both Statement I and Statement II are true
Statement I is false but Statement II is true
Statement I is true but Statement II is false
Explanation
Case I :
_24th_January_Morning_Shift_en_3_1.png)
$i+r=90^{\circ}$
Snell's law
$\mu_{a} \sin i=\mu_{g} \sin r$
$\tan i=\frac{\mu_{g}}{\mu_{a}}$
$i=\tan ^{-1}\left(\frac{\mu_{g}}{\mu_{a}}\right)=\theta_{B}$
Case II :
_24th_January_Morning_Shift_en_3_2.png)
$i+r=90^{\circ}$ as transmitted is $\perp$ to reflected.
$\tan i=\frac{\mu_{a}}{\mu_{g}} \Rightarrow i=\tan ^{-1} \frac{\mu_{a}}{\mu_{g}}=\frac{\pi}{2}-\theta_{B}$
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