\( P_1 \) and \( P_2 \) are two polaroids
The intensity of the unpolarised is \( I_0 \) and intensity of the transmitted light is \( \displaystyle\frac{3I_0}{8} \). The angle between axis of \( P_1 \) and \( P_2 \) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 30^\circ \)
The first polaroid passes half the intensity of unpolarised light, whatever its orientation. The light reaching \( P_2 \) is then polarised, and \( P_2 \) obeys Malus's law \( I = I_1\cos^{2}\theta \), where \( \theta \) is the angle between the two pass axes.
\( \displaystyle I_1 = \frac{I_0}{2} \)
\( \displaystyle I_2 = \frac{I_0}{2}\cos^{2}\theta = \frac{3I_0}{8} \)
\( \displaystyle \cos^{2}\theta = \frac{3}{4} \;\Rightarrow\; \cos\theta = \frac{\sqrt{3}}{2} \)
\( \displaystyle \theta = 30^\circ \)