Interference Light Waves Youngs Experiment Physics Wave Optics Class 12th Physics

Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio $\frac{I_{m a x} - I_{m i n}}{I_{m a x} + I_{m i n}}$ will be:

Option 1 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mroot> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </math> </span></p>

Option 2 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mroot> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </math> </span></p>

Option 3 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>2</mn> <mroot> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </math> </span></p>

Option 4 - <p><span class="mathml" contenteditable="false"> <math> <mrow> <mfrac> <mrow> <mn>2</mn> <mroot> <mrow> <mn>2</mn> <mi>x</mi> </mrow> <mrow></mrow> </mroot> </mrow> <mrow> <mi>x</mi> <mo>+</mo> <mn>1</mn> </mrow> </mfrac> </mrow> </math> </span></p>

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Vishal Baghel | Contributor-Level 10

6 months ago

Correct Option - 3

Detailed Solution:

$\frac{l_{m a x}}{l_{m i n}} = \frac{{(\sqrt[]{\frac{l_{1}}{l_{2}}} + 1)}^{2}}{{(\sqrt[]{\frac{l_{1}}{l_{2}}} - 1)}^{2}} \Rightarrow \frac{l_{m a x} - l_{m i n}}{l_{m a x} + l_{m i n}} = \frac{2 . \sqrt[]{\frac{l_{1}}{l_{2}}}}{\frac{l_{1}}{l_{2}} + 1} = \frac{2 \sqrt[]{2 x}}{2 x + 1}$

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For the setup shown in figure, the distance between slits much smaller as compared to the distance of slits from the screen. The total number of minimas on the screen are (where $d = 4 λ)$

Alok Kumar Singh

For minima

$d \cos ? θ = (n + \frac{1}{2}) λ$

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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:

Given, l₁ = 1

l₂ = 9l

case 1 $θ = \frac{π}{2}$

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

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case 2 q = p

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