Two coherent sources of intensity ratio of interfere in interference parteren $\frac{I_{max} - I_{min}}{I_{max} + I_{min}}$ is equal to

\frac{2 α}{1 + α}

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\frac{2 \sqrt{a}}{1 + α}

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\frac{2 α}{1 \sqrt{α}}

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\frac{1 + α}{2 α}

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Solution

The correct option is B $\frac{2 \sqrt{a}}{1 + α}$
$\begin{matrix} I_{max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}} I_{min} = I_{1} + I_{2} - 2 \sqrt{I_{1} I_{2}} ∴ \frac{I_{max} - I_{min}}{I_{max} + I_{min}} = \frac{4 \sqrt{I_{1} I_{2}}}{2 (I_{1} + I_{2})} = \frac{2 \sqrt{I_{1} I_{2}}}{(I_{1} + I_{2})} I_{1} = 1 I_{2} = α = \frac{2 \sqrt{α}}{1 + α} ∴ O p t i o n (B) i s c o r r e c t . \end{matrix}$

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Two coherent sources of intensity ratio of interfere in interference parteren Imax−IminImax+Imin is equal to

The correct option is B 2√a1+αImax=(√I1+√I2)2=I1+I2+2√I1I2Imin=I1+I2−2√I1I2∴Imax−IminImax+Imin=4√I1I22(I1+I2)=2√I1I2(I1+I2)I1=1I2=α=2√α1+α∴Option(B)iscorrect.

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