Two coherent sources of intensity ratio - interfere- Find the ratio - I max - I min - Imax - I min- in the interference pattern-A- 2 -1-B- -1-1-C- 2 p-1-D- -1-

A_1/a_2 =√(I_1/I_2 ) = √(β) I_max = ( √(I_1)+ √(I_2) )^2;I_min = ( √(I_1) √(I_2) )^2 I_max I_min/I_max + I_min = 4√(I_1)√(I_2)/2I_1+2I_2=2√(β)/1+β ...

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Byju's Answer

Standard XII

Physics

Intensity Amplitude Relationship

Two coherent ...

Question

Two coherent sources of intensity ratio $β$ interfere. Find the ratio $\frac{[I_{m a x} - I_{m i n}]}{[I_{m a x} + I_{m i n}]}$ in the interference pattern.

\frac{2 \sqrt{β}}{[1 + β]}

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\frac{2 β}{[1 + β]}

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[\frac{(\sqrt{β} + 1)}{(\sqrt{β} - 1)}]

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$\frac{\sqrt{β}}{(1 + \sqrt{β})}$

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Solution

The correct option is A $\frac{2 \sqrt{β}}{[1 + β]}$
$\frac{a_{1}}{a_{2}} = \sqrt{\frac{I_{1}}{I_{2}}} = \sqrt{β}$
$I_{m a x} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}; I_{m i n} = {(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}$
$\frac{I_{m a x} - I_{m i n}}{I_{m a x} + I_{m i n}} = \frac{4 \sqrt{I_{1}} \sqrt{I_{2}}}{2 I_{1} + 2 I_{2}} = \frac{2 \sqrt{β}}{1 + β}$

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