Arrange the following configurations of polarisers according to the magnitude of transmitted intensities through them in ascending order.
A. Two polarisers with their pass axes aligned
B. Two polarisers with their pass axes perpendicular to each other
C. Two polarisers with their pass axes making an angle of 75°
D. Two polarisers with their pass axes making an angle of 22.5°
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → B, C, D, A
When light passes a second polariser, the transmitted intensity follows Malus’s law, where \( \theta \) is the angle between the pass axes and \( I_1 \) is the intensity after the first polariser (\( I_0/2 \) for unpolarised light; the order does not depend on this).
\( \displaystyle I = I_1\cos^{2}\theta \)
Compare \( \cos^{2}\theta \) for each configuration:
\( \text{B: } \theta = 90^\circ,\; \cos^{2}\theta = 0 \)
\( \text{C: } \theta = 75^\circ,\; \cos^{2}\theta \approx 0.067 \)
\( \text{D: } \theta = 22.5^\circ,\; \cos^{2}\theta \approx 0.854 \)
\( \text{A: } \theta = 0^\circ,\; \cos^{2}\theta = 1 \)
The transmitted intensity decreases as the angle grows from 0° to 90°, so the ascending order is B, C, D, A.