The two light beams having intensities I and 9l interfere to produce a fringe pattern on a screen. The phase difference between the beams is /2 at point P and at point Q. Then the difference between the resultant intensities at P and Q will be:

Option 1 -

2 I

Option 2 -

6 I

Option 3 -

5 I

Option 4 -

7 I

2 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 2

Detailed Solution:

Given, l₁ = 1

l₂ = 9l

case 1 $θ = \frac{π}{2}$

$l_{P} = l_{1} + l_{2} + 2 \sqrt[]{l_{1} l_{2}} c o s θ$

= 10 l

case 2 q = p

$l_{Q} = l_{1} + l_{2} + 2 \sqrt[]{l_{1} l_{2}} c o s θ$

$= 10 l - 6 l$

$l_{P} - I_{Q} = 10 l - 4 l = 6 l$

Given, l1 = 1  l2 = 9lcase 1  <math> <mrow> <mi>θ</mi> <mo>=</mo> <mfrac> <mrow> <mi>π</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>   <math> <mrow> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mroot> <mrow> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow></mrow> </mroot> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </mrow> </math>  = 10 lcase 2 q = p <math> <mrow> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mi>Q</mi> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> <mo>+</mo> <mn>2</mn> <mroot> <mrow> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> <mrow></mrow> </mroot> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mi>θ</mi> </mrow> </math>   <math> <mrow> <mo>=</mo> <mn>1</mn> <mn>0</mn> <mtext> </mtext> <mtext> </mtext> <mi>l</mi> <mo>−</mo> <mn>6</mn> <mtext> </mtext> <mtext> </mtext> <mi>l</mi> </mrow> </math>                <math> <mrow> <msub> <mrow> <mi>l</mi> </mrow> <mrow> <mi>P</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>I</mi> </mrow> <mrow> <mi>Q</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mn>0</mn> <mtext> </mtext> <mtext> </mtext> <mi>l</mi> <mo>−</mo> <mn>4</mn> <mtext> </mtext> <mtext> </mtext> <mi>l</mi> <mo>=</mo> <mn>6</mn> <mtext> </mtext> <mtext> </mtext> <mi>l</mi> </mrow> </math>

0 Upvotes 0 Downvotes

The two light beams having intensities I and 9l interfere to produce a fringe pattern on a screen. The phase difference between the beams is /2 at point P and at point Q. Then the difference between the resultant intensities at P and Q will be:

1 Answer

Similar Questions for you

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