MHT CET · Physics · Wave Optics
A beam of unpolarized light passes through a tourmaline crystal A and then it passes through a second tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of emergent light is \(\mathrm{I}_0\). Now \(B\) is rotated by \(45^{\circ}\) about the ray. The emergent light will have intensity \(\left(\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)\)
- A \(\frac{I_0}{2}\)
- B \(\frac{I_0}{\sqrt{2}}\)
- C \(\frac{\sqrt{2}}{I_0}\)
- D \(\frac{2}{I_0}\)
Answer & Solution
Correct Answer
(A) \(\frac{I_0}{2}\)
Step-by-step Solution
Detailed explanation
Using law of Malus,
\(\begin{aligned}
\mathrm{I} & =\mathrm{I}_0 \cos ^2 \theta \\
& =\mathrm{I}_0\left(\cos ^2 45\right) \\
& =\mathrm{I}_0\left(\frac{1}{\sqrt{2}}\right)^2 \\
& =\frac{\mathrm{I}_0}{2}
\end{aligned}\)
\(\begin{aligned}
\mathrm{I} & =\mathrm{I}_0 \cos ^2 \theta \\
& =\mathrm{I}_0\left(\cos ^2 45\right) \\
& =\mathrm{I}_0\left(\frac{1}{\sqrt{2}}\right)^2 \\
& =\frac{\mathrm{I}_0}{2}
\end{aligned}\)
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