Two polaroids are placed with their optiic axis perpendicular to each other. One of them is rotated through 45 degrees then what is the intensity of light emerging from the second polaroid if I_{o} is the intensity of the unpolarised light?

When this light is passes through first polarizer then its intensity becomes $\frac{{I}_{o}}{2}$

Now the angle between the first polarizer and second polarizer is ${45}^{0}$

Thus final intensity becomes $I=\frac{{I}_{o}}{2}{\mathrm{cos}}^{2}\left(45\right)=\frac{{I}_{o}}{2}\times {\left(\frac{1}{\sqrt{2}}\right)}^{2}=\frac{{I}_{0}}{4}$

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