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(C) The intensity of light passing through a pair of polarizers is given by Malus' Law: $I = I_0 \cos^2 	heta$,where $	heta$ is the angle between th

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$(i) > (iii) > (ii) > (iv)$

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(C) The intensity of light passing through a pair of polarizers is given by Malus' Law: $I = I_0 \cos^2 	heta$,where $	heta$ is the angle between the transmission axes of the two polarizers.For unpolarized light incident on the first polarizer,the intensity becomes $I_1 = I_0 / 2$. The intensity after the second polarizer is $I = I_1 \cos^2 	heta = (I_0 / 2) \cos^2 	heta$.To rank the pairs,we calculate the angle $	heta$ between the two sheets for each case:$(i)$ The first sheet is at $30^\circ$ to the vertical,the second is at $60^\circ$ to the horizontal. The angle between them is $	heta = 90^\circ - 30^\circ - 60^\circ = 0^\circ$. Thus,$\cos^2(0^\circ) = 1$.(ii) The first sheet is at $30^\circ$ to the vertical,the second is at $60^\circ$ to the horizontal. The angle between them is $	heta = 60^\circ$. Thus,$\cos^2(60^\circ) = 0.25$.(iii) The first sheet is at $30^\circ$ to the horizontal,the second is at $60^\circ$ to the horizontal. The angle between them is $	heta = 30^\circ$. Thus,$\cos^2(30^\circ) = 0.75$.(iv) The first sheet is at $30^\circ$ to the horizontal,the second is at $60^\circ$ to the horizontal. The angle between them is $	heta = 90^\circ$. Thus,$\cos^2(90^\circ) = 0$.Comparing the values: $1 > 0.75 > 0.25 > 0$,which corresponds to $(i) > (iii) > (ii) > (iv)$.

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