Two beams,A and B,of plane polarized light wi | vedclass

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(C) According to Malus's law,the intensity of the emerging beam is given by $I = I_0 \cos^2 	heta$.Let the initial intensity of beam $A$ be $I_A$ and

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$\frac{1}{3}$

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(C) According to Malus's law,the intensity of the emerging beam is given by $I = I_0 \cos^2 	heta$.Let the initial intensity of beam $A$ be $I_A$ and beam $B$ be $I_B$. When the polaroid is at the position where beam $A$ has maximum intensity,the angle between the transmission axis of the polaroid and the plane of polarization of beam $A$ is $0^{\circ}$,and for beam $B$ it is $90^{\circ}$.After rotating the polaroid by $30^{\circ}$,the new angle for beam $A$ is $	heta_A = 30^{\circ}$ and for beam $B$ is $	heta_B = 90^{\circ} - 30^{\circ} = 60^{\circ}$.The intensities of the beams after passing through the polaroid are:$I_A' = I_A \cos^2(30^{\circ}) = I_A \left(\frac{\sqrt{3}}{2}ight)^2 = I_A \cdot \frac{3}{4}$$I_B' = I_B \cos^2(60^{\circ}) = I_B \left(\frac{1}{2}ight)^2 = I_B \cdot \frac{1}{4}$Given that the beams appear equally bright,$I_A' = I_B'$:$I_A \cdot \frac{3}{4} = I_B \cdot \frac{1}{4}$$\frac{I_A}{I_B} = \frac{1}{3}$

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