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Q.

A beam of ordinary light is incident on a system of four polaroids which are arranged in succession such that each polaroid is turned through 30º with respect to the preceding one. The percentage of the incident intensity that emerges out from the system is approximately

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a

21%

b

14%

c

6.25%

d

56%

answer is C.

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Detailed Solution

No of polaroids are 4. Intensity of emerging light
$\begin{array}{l} I = \frac{I_{0}}{2} \cos^{2} θ_{1} \cos^{2} θ_{2} \cos^{2} θ_{3} \\ = \frac{I_{0}}{2} \cos^{2} 30^{0} \cos^{2} 30^{0} \cos^{2} 30^{0} \\ = \frac{I_{0}}{2} \times \frac{3}{4} \times \frac{3}{4} \times \frac{3}{4} = \frac{27 I_{0}}{128} \\ \Rightarrow \frac{I}{I_{0}} \times 100 = \frac{27}{128} \times 100 = 21 % \end{array}$

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