\( P_1, P_2, P_3 \) are three Polaroid sheets, \( P_1 \) and \( P_3 \) are two crossed polaroids. What should be the angle between Polaroids \( P_1 \) and \( P_2 \), so that the value of \( I' = I_o/4 \)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \theta = \pi/4 \)
The light leaving \( P_1 \) has intensity \( I_o \) and is plane polarised. Each later polaroid follows Malus's law, \( I = I_{\text{in}}\cos^{2}\phi \). Since \( P_1 \) and \( P_3 \) are crossed, if \( P_2 \) makes angle \( \theta \) with \( P_1 \), it makes \( 90^\circ - \theta \) with \( P_3 \).
\( \displaystyle I_2 = I_o\cos^{2}\theta \)
\( \displaystyle I' = I_o\cos^{2}\theta\,\cos^{2}(90^\circ - \theta) = I_o\cos^{2}\theta\,\sin^{2}\theta \)
\( \displaystyle I' = \frac{I_o}{4}\,\sin^{2}2\theta \)
For \( I' = I_o/4 \):
\( \displaystyle \sin^{2}2\theta = 1 \;\Rightarrow\; 2\theta = \frac{\pi}{2} \;\Rightarrow\; \theta = \frac{\pi}{4} \)
This is also the largest intensity that can pass the crossed pair with a polaroid between them.
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
NCERT (2026-27):
Polarisation – …
