A polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is just <math> <mn>10</mn> <mi mathvariant="normal">%</mi> </math> <math></math>&nbsp;of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero is

<math> <msup> <mrow> <mrow> <mn>90</mn> </mrow> </mrow> <mrow> <mrow> <mo>∘</mo> </mrow> </mrow> </msup> </math> wave optics

Ask & Answer Question

Physics Class 12th Physics Wave Optics

A polarizer-analyser set is adjusted such that the intensity of light coming out of the analyser is just $10 %$ of the original intensity. Assuming that the polarizer-analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero is

Option 1 -

${18.4}^{\circ}$

Option 2 -

${71.6}^{\circ}$

Option 3 -

$45^{\circ}$

Option 4 -

$90^{\circ}$ wave optics

2 Views | Posted 2 months ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$I = I_{0} {c o s}^{2} ? θ$

$\frac{I_{0}}{10} = I_{0} {c o s}^{2} ? θ$

$c o s ? θ = \frac{1}{\sqrt[]{10}} = 0.31 < \frac{1}{\sqrt[]{2}}$ which is 0.707

So, $θ > 45^{?}$ $^{}$ and $90 - θ < 45^{?}$ $^{}$ so only one option is correct i.e. ${18.4}^{?}$ $^{}$

Angle rotated should be $= 90^{?} - {71.6}^{?} = {18.4}^{?}$ $^{}^{}^{}$ .

<math> <mrow> <mi mathvariant="normal"> </mi> </mrow> <mi>I</mi> <mo>=</mo> <msub> <mrow> <mrow> <mi>I</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <msup> <mrow> <mrow> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>? </mo> <mi>θ</mi> </math> <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi mathvariant="normal">I</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <msub> <mrow> <mrow> <mi mathvariant="normal">I</mi> </mrow> </mrow> <mrow> <mrow> <mn>0</mn> </mrow> </mrow> </msub> <msup> <mrow> <mrow> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>? </mo> <mi>θ</mi> </math> <math> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">s</mi> <mo>? </mo> <mi>θ</mi> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>0.31</mn> <mo><</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> <mrow></mrow> </mroot> </mrow> </mrow> </mfrac> </math> which is 0.707So, <math> <mi>θ</mi> <mo>></mo> <msup> <mrow> <mrow> <mn>45</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> and <math> <mn>90</mn> <mo>-</mo> <mi>θ</mi> <mo><</mo> <msup> <mrow> <mrow> <mn>45</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> so only one option is correct i.e. <math> <msup> <mrow> <mrow> <mn>18.4</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math>Angle rotated should be <math> <mo>=</mo> <msup> <mrow> <mrow> <mn>90</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> <mo>-</mo> <msup> <mrow> <mrow> <mn>71.6</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mrow> <mn>18.4</mn> </mrow> </mrow> <mrow> <mrow> <mo>? </mo> </mrow> </mrow> </msup> </math> <math><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup><msup><mrow><mrow></mrow></mrow><mrow><mrow></mrow></mrow></msup></math> .

0 Upvotes 0 Downvotes

Get authentic answers from experts, students and alumni that you won't find anywhere else

On Shiksha, get access to

65k Colleges
1.2k Exams
679k Reviews
1800k Answers

Community GuidelinesUser Points System

QuestionsDiscussionsTags

1 Answer

Learn more about...

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question