Two coherent sources of intensity ratio - interfere- then Imax-IminImax-Imin is equal to

The correct option is B 2√(β)1+β I_1I_2=β I_max=I_1+I_2+2√(I_1I_2) =I_1+β I_1+2√(β I_1) =I_1+β I_1+2√(β)I_1 I_min=I_1+I_2 2√(I_1I ...

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Standard XII

Physics

Time Period of Pendulum

Two coherent ...

Question

Two coherent sources of intensity ratio $β$ interfere, then $\frac{I_{m a x} - I_{m i n}}{I_{m a x} + I_{m i n}}$ is equal to

\frac{β}{1 + β}

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\frac{2 \sqrt{β}}{1 + β}

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\frac{2 \sqrt{β}}{1 + \sqrt{β}}

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\frac{2 β}{1 + \sqrt{β}}

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Solution

The correct option is B $\frac{2 \sqrt{β}}{1 + β}$
$\frac{I_{1}}{I_{2}} = β$

$I_{m a x} = I_{1} + I_{2} + 2 \sqrt{I_{1} I_{2}}$
$= I_{1} + β I_{1} + 2 \sqrt{β I_{1}}$
$= I_{1} + β I_{1} + 2 \sqrt{β} I_{1}$

$I_{m i n} = I_{1} + I_{2} - 2 \sqrt{I_{1} I_{2}} = I_{1} + β I_{1} - 2 \sqrt{β} I_{1}$

$\frac{I_{m a x} - I_{m i n}}{I_{m a x} + I_{m i n}} = \frac{I_{1} β I_{1} + 2 \sqrt{β} I_{1} - I_{1} - β I_{1} + 2 \sqrt{β} I_{1}}{I_{1} + β I_{1} + 2 \sqrt{β} I_{1} + I_{1} + β I_{1} - 2 \sqrt{β} I_{1}}$
$= \frac{4 \sqrt{β} I_{1}}{2 I_{1} + 2 β I_{1}}$
$= \frac{2 \sqrt{β}}{1 + β}$

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Two coherent sources of intensity ratio β interfere, then Imax−IminImax+Imin is equal to

The correct option is B 2√β1+βI1I2=βImax=I1+I2+2√I1I2=I1+βI1+2√βI1=I1+βI1+2√βI1Imin=I1+I2−2√I1I2=I1+βI1−2√βI1Imax−IminImax+Imin=I1βI1+2√βI1−I1−βI1+2√βI1I1+βI1+2√βI1+I1+βI1−2√βI1=4√βI12I1+2βI1=2√β1+β

Two coherent sources of intensity ratio $β$ interfere, then $\frac{I_{m a x} - I_{m i n}}{I_{m a x} + I_{m i n}}$ is equal to