A prism has refracting angle of 30⁰ and it is made of glass of refractive index $\sqrt[]{2}$ . At what angle should a light ray be incident on a face of prism such that it passes normally through the other face?

Correct Option - 3


Detailed Solution:

For normal emergence

$r=A$

From Snell’s Law

$\frac{\sin ?i}{\sin ?r}=\frac{\mu }{1}$

$?\sin ?i=\sqrt[]{2}\sin ?{30}^0$

$?i={45}^0$

<div><div><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1758176199phpbyUAzQ.jpeg" alt="" width="277" height="226" loading="lazy"></picture></div></div><p>For normal emergence</p><p><span contenteditable="false"> <math> <mi>r</mi> <mo>=</mo> <mi>A</mi> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p>From Snell’s Law</p><p><span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <mi>i</mi> </mrow> </mrow> </mrow> </mrow> <mrow> <mrow> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <mi>r</mi> </mrow> </mrow> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mi>μ</mi> </mrow> </mrow> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> </mfrac> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mo>? </mo> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <mi>i</mi> <mo>=</mo> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mrow> <mrow> <mi mathvariant="normal">sin</mi> </mrow> <mo>? </mo> <mrow> <msup> <mrow> <mrow> <mn>30</mn> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mrow> </mrow> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p><p><span contenteditable="false"> <math> <mo>? </mo> <mi>i</mi> <mo>=</mo> <msup> <mrow> <mrow> <mn>45</mn> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msup> </math> </span><br>&lt;!- [endif]-&gt;&lt;!- [endif]-&gt;</p>

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