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 π 3 and π 2 , respectively are

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The formula to calculate the intensity of the interference pattern in Young's double slit experiment can be written as
$I = 4 I_{0} \cos^{2} (\frac{ϕ}{2}) . . . (1)$
Hence, the ratio of the required intensities can be calculated as follows-
$\begin{array}{rcl} \frac{I_{1}}{I_{2}} & = & \frac{4 I_{0} \cos^{2} (\frac{π}{6})}{4 I_{0} \cos^{2} (\frac{π}{4})} \\ = & \frac{\frac{3}{4}}{\frac{1}{2}} \\ = & \frac{3}{2} \end{array}$

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