First slide

Young's double slit Experiment

Question

Statement 1: In Young's experiment, for two coherent sources, the resultant intensity is given by $I = 4 I_{0} \cos^{2} \frac{ϕ}{2}$ .
Statement 2: Ratio of maximum to minimum intensity is $\frac{I_{max}}{I_{min}} = \frac{{(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}}{{(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}} .$

Moderate

A

Both statements 1 and 2 are correct
B

Statement 1 is correct statement 2 is incorrect
C

Statement 1 is incorrect statement 2 is correct
D

Both statements 1 and 2 are incorrect

Solution

For two coherent sources,
$I = I_{1} + I_{2} + \sqrt{I_{1} I_{2}} cosθ$
Putting, $I_{1} = I_{2} = I_{0}$
We have $I = I_{0} + I_{0} + 2 \sqrt{I_{0} \times I_{0}} cosϕ$
Simplifying the above expression
$I = 2 I_{0} (1 + \cos ϕ)$
$= 2 I_{0} (1 + 2 c o s^{2} \frac{ϕ}{2} - 1)$
$= 2 I_{0} \times 2 \cos^{2} \frac{ϕ}{2} = 4 I_{0} \cos^{2} \frac{ϕ}{2}$
Also, $I_{max} = {(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}$
$I_{min} = (\sqrt{I_{1}} + \sqrt{I_{2}})$
$∴ \frac{I_{max}}{I_{min}} = \frac{{(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}}{{(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}}$

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