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PhysicsWave OpticsMiscellaneousEasy2 minPYQ_2020

PhysicsEasysingle choice

Consider an interference pattern between two coherent sources. If $I_{1}$ and $I_{2}$ be intensities at points where the phase difference are $\frac{π}{3}$ and $\frac{2 π}{3}$ respectively, then the intensity at maxima is

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Answer:

Solution:

$I_{1} = I_{A} + I_{B} + 2 \sqrt{I_{A} I_{B}} cos \frac{π}{3}$ ...(1)

$I_{2} = I_{A} + I_{B} + 2 \sqrt{I_{A} I_{B}} cos \frac{2 π}{3}$ ...(2)

$\Rightarrow$ $I_{1} + I_{2} = 2 (I_{A} + I_{B})$ ...(3)

From (1)

$\Rightarrow$ $I_{1} = \frac{I_{1} + I_{2}}{2} + \sqrt{I_{A} I_{B}}$

$I_{1} - (\frac{I_{1} + I_{2}}{2}) = \sqrt{I_{A} I_{B}}$

$\frac{I_{1} - I_{2}}{2} = \sqrt{I_{A} I_{B}}$

$I_{max} = {(\sqrt{I_{A}} + \sqrt{I_{B}})}^{2}$

$= I_{A} + I_{B} + 2 \sqrt{I_{A} I_{B}}$ ...(4)

$I_{max} = \frac{I_{1} + I_{2}}{2} + (I_{1} - I_{2})$

$= \frac{3 I_{1} - I_{2}}{2}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Wave OpticsSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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