A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:

Option 1 -

$10 °$

Option 2 -

$20 °$

Option 3 -

$30 °$

Option 4 -

$60 °$

2 Views | Posted 3 months ago

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1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

3 months ago

Correct Option - 4

Detailed Solution:

Velocity of light in medium 2

$= \frac{1}{\sqrt[]{μ_{m} \in_{m}}}$

$v_{2} = \frac{1}{\sqrt[]{μ_{0} μ_{r} \in_{0} \in_{r}}}$

$= \frac{1}{\sqrt[]{1 \times μ_{0} \in_{0} \times 4}}$

$v_{2} = \frac{1}{2 \sqrt[]{μ_{0} \in_{0}}}$

By snell’s law for total internal Reflection

$μ_{2} s i n θ_{C} > μ_{1} s i n 90 °$

$θ_{c} > 30 °$

Velocity of light in medium 2 <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>m</mi> </mrow> </msub> <msub> <mrow> <mo>∈</mo> </mrow> <mrow> <mi>m</mi> </mrow> </msub> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math> <img > <math> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>r</mi> </mrow> </msub> <msub> <mrow> <mo>∈</mo> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <msub> <mrow> <mo>∈</mo> </mrow> <mrow> <mi>r</mi> </mrow> </msub> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math> <math> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mroot> <mrow> <mn>1</mn> <mo>×</mo> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <msub> <mrow> <mo>∈</mo> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <mo>×</mo> <mn>4</mn> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mroot> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>0</mn> </mrow> </msub> <msub> <mrow> <mo>∈</mo> </mrow> <mrow> <mn>0</mn> </mrow> </msub> </mrow> <mrow></mrow> </mroot> </mrow> </mfrac> </mrow> </math> By snell’s law for total internal Reflection <math> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mi>C</mi> </mrow> </msub> <mo>></mo> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>9</mn> <mn>0</mn> <mo>°</mo> </mrow> </math> <math> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> <mo>></mo> <mn>3</mn> <mn>0</mn> <mo>°</mo> </mrow> </math>

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A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:

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