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AIIMS 2016
Exam
AIIMS
Year
2016
Subject
Physics
Chapter
Wave Optics

AIIMS 2016 · Physics · Wave Optics

The two coherent sources with intensity ratio β produce...

The two coherent sources with intensity ratio β\beta produce interference. The fringe visibility will be

Options

  1. A2β1+β\frac{2 \sqrt{\beta}}{1+\beta}
  2. B2β2 \beta
  3. C2(1+β)\frac{2}{(1+\beta)}
  4. Dβ1+β\frac{\sqrt{\beta}}{1+\beta}

Correct answer

A. 2β1+β\frac{2 \sqrt{\beta}}{1+\beta}

Step-by-step solution

I1I2=a2b2=β∴ab=β\frac{I_1}{I_2}=\frac{a^2}{b^2}=\beta \quad \therefore \frac{a}{b}=\sqrt{\beta} Fringe visibility is given by V=Imax⁡−Imin⁡Imax⁡+Imin⁡=(a+b)2−(a−b)2(a+b)2+(a−b)2=4ab2(a2+b2)=2(a/b)(a2b2+1)=2ββ+1\begin{aligned} V= & \frac{I_{\max }-I_{\min }}{I_{\max }+I_{\min }}=\frac{(a+b)^2-(a-b)^2}{(a+b)^2+(a-b)^2} \\ & =\frac{4 a b}{2\left(a^2+b^2\right)}=\frac{2(a / b)}{\left(\frac{a^2}{b^2}+1\right)}=\frac{2 \sqrt{\beta}}{\beta+1}\end{aligned}
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