KCET · Physics · Wave Optics
An unpolarised light of intensity \(I\) is passed through two polaroids kept one after the other with their planes parallel to each other. The intensity of light emerging from second polaroid is \(\frac{I}{4}\). The angle between the pass axes of the polaroids is
- A \(45^{\circ}\)
- B \(0^{\circ}\)
- C \(60^{\circ}\)
- D \(30^{\circ}\)
Answer & Solution
Correct Answer
(A) \(45^{\circ}\)
Step-by-step Solution
Detailed explanation
The given situation is shown in the figure.
According to law of Malus,
\(\begin{aligned} I^{\prime} & =\left(\frac{I}{2}\right) \cos ^2 \theta \\ \Rightarrow \quad \frac{I}{4} & =\frac{I}{2} \cos ^2 \theta \\ \Rightarrow \cos ^2 \theta & =\frac{1}{2} \\ \Rightarrow \cos \theta & =\frac{1}{\sqrt{2}} \\ \Rightarrow \quad \theta & =45^{\circ}\end{aligned}\)
According to law of Malus,
\(\begin{aligned} I^{\prime} & =\left(\frac{I}{2}\right) \cos ^2 \theta \\ \Rightarrow \quad \frac{I}{4} & =\frac{I}{2} \cos ^2 \theta \\ \Rightarrow \cos ^2 \theta & =\frac{1}{2} \\ \Rightarrow \cos \theta & =\frac{1}{\sqrt{2}} \\ \Rightarrow \quad \theta & =45^{\circ}\end{aligned}\)
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