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Question: The two coherent source with intensity ratio \(\beta\)produced interference. The fringe visibility w...

The two coherent source with intensity ratio β\betaproduced interference. The fringe visibility will be:

A

2β1+β\frac{2\sqrt{\beta}}{1 + \beta}

B

2β2\beta

C

2(1+β)\frac{2}{(1 + \beta)}

D

β1+β\frac{\sqrt{\beta}}{1 + \beta}

Answer

2β1+β\frac{2\sqrt{\beta}}{1 + \beta}

Explanation

Solution

I1I2=a2b2=β∴ab=β\frac{I_{1}}{I_{2}} = \frac{a^{2}}{b^{2}} = \beta\therefore\frac{a}{b} = \sqrt{\beta}

Fringe visibility is given by

=4ab2(a2+b2)=2(a/b)(a2b2+1)=2Bβ+1= \frac{4ab}{2(a^{2} + b^{2})} = \frac{2(a/b)}{\left( \frac{a^{2}}{b^{2}} + 1 \right)} = \frac{2\sqrt{B}}{\beta + 1}