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(B) Let the initial intensity of the unpolarized light from the source be $I_0.$ When this light passes through the first Polaroid $P_1,$ the intensit

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$30$

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(B) Let the initial intensity of the unpolarized light from the source be $I_0.$ When this light passes through the first Polaroid $P_1,$ the intensity becomes $I_1 = I_0/2.$ Given that the intensity on the screen is $I/2,$ we assume the initial intensity $I$ refers to the intensity after passing through $P_1$ or that $I_0 = I.$ Let the intensity after $P_1$ be $I' = I/2.$According to Malus' Law,the intensity of light after passing through the second Polaroid $P_2$ is given by $I_{final} = I' \cos^2 \phi,$ where $\phi$ is the angle between the transmission axes of $P_1$ and $P_2.$Initially,the intensity is $I/2,$ which implies $\cos^2 \phi = 1,$ so $\phi = 0^\circ.$We want the final intensity to be $3I/8.$ Substituting the values:$3I/8 = (I/2) \cos^2 \phi$$\cos^2 \phi = (3I/8) 	imes (2/I) = 3/4$$\cos \phi = \sqrt{3}/2$$\phi = 30^\circ.$Thus,$P_2$ should be rotated by an angle of $30^\circ.$

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