KCET · Physics · Wave Optics

Three polaroid sheets \(P_{1}, P_{2}\) and \(P_{3}\) are kept parallel to each other such that the angle between pass axes of \(P_{1}\) and \(P_{2}\) is \(45^{\circ}\) and that between \(P_{2}\) and \(P_{3}\) is \(45^{\circ}\). If unpolarised beam of light of intensity \(128 \mathrm{Wm}^{-2}\) is incident on \(P_{1}\). What is the intensity of light coming out of \(P_{3}\) ?

A \(128 \mathrm{Wm}^{-2}\)
B zero
C \(16 \mathrm{Wm}^{-2}\)
D \(64 \mathrm{Wm}^{-2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(16 \mathrm{Wm}^{-2}\)

Step-by-step Solution

Detailed explanation

The situation given in question can be shown as

Here, \(I_{0}=128 \mathrm{Wm}^{-2}, \theta_{1}=45^{\circ}\) and \(\theta_{2}=45^{\circ}\)
According to Malus's law, intensity of the light coming out of \(P_{2}\),
\(I=\frac{I_{0}}{2} \cos ^{2} \theta_{1}\)
Similarly, intensity of light coming out of \(P_{3}\),
\(\begin{aligned}
I^{\prime} &=\frac{I_{0}}{2} \cos ^{2} \theta_{1} \cos ^{2} \theta_{2} \\
&=\frac{128}{2} \times \cos ^{2} 45^{\circ} \times \cos ^{2} 45^{\circ} \\
&=64 \times \frac{1}{2} \times \frac{1}{2}=16 \mathrm{Wm}^{-2}
\end{aligned}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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