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(C) The light is partially polarized. The intensities along the principal axes are $I_y = I_0$ and $I_x = \frac{2I_0}{3}$.When a polaroid is placed wi

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$\frac{5}{6}I_0$

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(C) The light is partially polarized. The intensities along the principal axes are $I_y = I_0$ and $I_x = \frac{2I_0}{3}$.When a polaroid is placed with its pass axis at an angle $	heta = 45^{\circ}$ to the $y$-axis, the transmitted intensity $I$ is given by the sum of the components of the intensities along the pass axis:$I = I_y \cos^2(45^{\circ}) + I_x \cos^2(45^{\circ})$Substituting the given values:$I = I_0 \left(\frac{1}{\sqrt{2}}ight)^2 + \frac{2I_0}{3} \left(\frac{1}{\sqrt{2}}ight)^2$$I = I_0 \cdot \frac{1}{2} + \frac{2I_0}{3} \cdot \frac{1}{2}$$I = \frac{I_0}{2} + \frac{I_0}{3} = \frac{3I_0 + 2I_0}{6} = \frac{5I_0}{6}$

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