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  • The ratio of intensities at two points P and Q on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are <img alt="\frac{\pi }{3}"

The ratio of intensities at two points P and Q on the screen in a Young's double slit experiment where phase
difference between two waves of same amplitude are \frac{\pi }{3} and \frac{\pi }{2}, respectively are

Option: 1

3:2


Option: 2

3:1


Option: 3

2:3


Option: 4

1:3


Answers (1)

best_answer

\begin{aligned} & \mathrm{I}_{\mathrm{res}}=4 \mathrm{I}_0 \cos ^2\left(\frac{\theta}{2}\right) \\ & \text { If } \theta=\frac{\pi}{3}, \\ & I_{\mathrm{res}}=4 \mathrm{I}_{\mathrm{o}}, \cos ^2\left[\frac{\pi}{6}\right] \\ & =4 \mathrm{I}_0 \cdot\left(\frac{\sqrt{3}}{2}\right)^2 \\ & \end{aligned}

\begin{aligned} &I_1=\left(4 I_0\right)\left(\frac{3}{4}\right)=3 I_0\\ \end{aligned}

\begin{aligned} &\text { If } \theta=\frac{\pi}{2}, \\ I_{\text {res }} & =4 I_0 \cdot \cos ^2\left(\frac{\pi}{2}\right) \\ & =4 I_0\left(\frac{1}{\sqrt{2}}\right)^2 \\ & =\left(4 I_0\right)\left(\frac{1}{2}\right) \end{aligned}

\begin{gathered} \mathrm{I}_2=2 \mathrm{I}_0 \\ \frac{\mathrm{I}_1}{\mathrm{I}_2}=\frac{3}{2} \end{gathered}

Posted by

Deependra Verma

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