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A point source S emits unpolarized light uniformly in all directions. At two points A and B, the ratio $r = I_{A} / I_{B}$ of the intensities of light is 2. If a set of two polaroids having $45^{0}$ angle between their pass-axes is placed just before point B, then the new value of r will be _____.

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answer is 8.

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Detailed Solution

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$I α \frac{1}{I^{2}}$
Where I: distance from point source.
$\Rightarrow \frac{I_{A}}{I_{B}} = \frac{I_{B}^{2}}{I_{A}^{2}} = 2$
$\Rightarrow I_{B} = \sqrt{2} I_{A} ......... (1)$
Also, due to polaroids: $\Rightarrow I_{B}^{'} = \frac{I_{B}}{2} \cos^{2} 45^{0} = \frac{I_{B}}{4}$
$\Rightarrow I_{B}^{'} = \frac{I_{B}}{4} ........ (2)$
Ratio becomes 4 times.
$\Rightarrow r_{n e w} = 8$

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