An unpolarized light of certain intensity passes through a combination of two polarisers whose transmission axes are at

Question

An unpolarized light of certain intensity passes through a combination of two polarisers whose transmission axes are at $30 °$ and $90 °$ , respectively, with respect to the horizontal axis. A third polariser with its transmission axis at $60 °$ with the horizontal axis is placed between the two existing polarisers. The ratio of the output intensities with and without the third polariser is _________. [2026]

Smart Achievers · Accepted Answer

(3)

$90 °$

$I_{2} = (\frac{I_{0}}{2}) \cos^{2} 30 ° = (\frac{I_{0}}{2}) (\frac{3}{4}) = \frac{3 I_{0}}{8}$

$I_{3} = \frac{3 I_{0}}{8} \cdot \frac{3}{4} = \frac{9 I_{0}}{32}$

without 3rd polariser,

$I_{3}' = (\frac{I_{0}}{2}) \cos^{2} 60 ° = \frac{I_{0}}{2} \times \frac{1}{4} = \frac{I_{0}}{8}$

$\frac{I_{3}}{I_{3}'} = \frac{9}{32} \times 8 = \frac{9}{4}$

Solution

1 $\frac{3}{4}$

2 $\frac{4}{3}$

3 $\frac{9}{4}$

4 $\frac{4}{9}$

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Solution

1 34

2 43

3 94

4 49

Ans. (3) I1=I02 I2=(I02)cos230°=(I02)(34)=3I08 I3=3I08·34=9I032 without 3rd polariser, I3'=(I02)cos260°=I02×14=I08 I3I3'=932×8=94

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1 $\frac{3}{4}$

2 $\frac{4}{3}$

3 $\frac{9}{4}$

4 $\frac{4}{9}$