Class 11th Physics Units and Measurement

The speed of light in media 'A' and 'B' are 2.0 * 10¹⁰ cm/s and 1.5 * 10¹⁰ cm/s respectively. A ray of light enters from the medium B to an incident angle 'q'. If the ray suffers total internal reflection, then

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>s</mi> <mi>i</mi> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>θ</mi> <mo>></mo> <mi>s</mi> <mi>i</mi> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>θ</mi> <mo><</mo> <mi>s</mi> <mi>i</mi> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mi>θ</mi> <mo>></mo> <mi>s</mi> <mi>i</mi> <msup> <mrow> <mi>n</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p>

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Answered by

Alok Kumar Singh | Contributor-Level 10

8 months ago

Correct Option - 4

Detailed Solution:

$\frac{s i n θ_{C}}{V_{B}} = \frac{s i n 90 °}{V_{A}} \Rightarrow s i n θ_{C} = \frac{V_{B}}{V_{A}} = \frac{1.5 * 1 0^{10}}{2.0 * 1 0^{10}} = \frac{3}{4}$

According to question, we can write

$θ > θ = s i n^{- 1} (\frac{3}{4})$

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