Two circularly shaped linear polarisers are placed coaxially. The transmission axis of the first polarizer is at $30^{\circ}$ from the vertical while the second one is at $60^{\circ}$, both in the clockwise sense. If an unpolarised beam of light of intensity $\mathrm{I}=20 \mathrm{~W} / \mathrm{m}^{2}$ is incident on this pair of polarisers, then the intensities $\mathrm{I}_{1}$ and $\mathrm{I}_{2}$ transmitted by the first and the second polarisers, respectively, will be close to

• Correct answer
  A

  $\mathrm{I}_{1}=10.0 \mathrm{~W} / \mathrm{m}^{2}$ and $\mathrm{I}_{2}=7.5 \mathrm{~W} / \mathrm{m}^{2}$
• B

  $\mathrm{I}_{1}=20.0 \mathrm{~W} / \mathrm{m}^{2}$ and $\mathrm{I}_{2}=15 \mathrm{~W} / \mathrm{m}^{2}$
• C

  $\mathrm{I}_{1}=10.0 \mathrm{~W} / \mathrm{m}^{2}$ and $\mathrm{I}_{2}=8.6 \mathrm{~W} / \mathrm{m}^{2}$
• D

  $\mathrm{I}_{1}=15.0 \mathrm{~W} / \mathrm{m}^{2}$ and $\mathrm{I}_{2}=0.0 \mathrm{~W} / \mathrm{m}^{2}$

Solution

$\begin{aligned} \mathrm{I}_{0} &=20 \mathrm{~W} / \mathrm{m}^{2} \\ \mathrm{I}_{1} &=\frac{\mathrm{I}_{0}}{2}=\frac{20}{2}=10 \mathrm{~W} / \mathrm{m}^{2} \\ \mathrm{I}_{2} &=\mathrm{I}_{1} \cos ^{2} 30^{\circ} \\ &=10\left(\frac{\sqrt{3}}{2}\right)^{2}=10 . \frac{3}{4} \\ &=7.5 \mathrm{w} / \mathrm{m}^{2} \end{aligned}$

Hence, the correct answer is option: 'A'.