Two beams, \(A\) and \(B\), of plane-polarized light with mutually perpendicular planes of polarization are seen through a Polaroid. From the position when beam \(A\) and has maximum intensity (and beam \(B\) has zero intensity), a rotation of polaroid through \(30^\circ\) makes the two beams appear equally bright. If the initial intensities of the two beams are \(I_A\) and \(I_B\) respectively, then \(\dfrac{I_A}{I_B}\) equals:
1. \(\dfrac{3}{2}\)
2. \(1\)
3. \(\dfrac{1}{3}\)
4. \(3\)

Unpolarized light of intensity \(I\) passes through an ideal polarizer \(A\). Another identical polarizer \(B\) is placed behind \(A\). The intensity of light beyond \(B\) is found to be \(\frac{I}{2}\). Now another identical polarizer \(C\) is placed between \(A\) and \(B\). The intensity beyond \(B\) is now found to be \(\frac{I}{8}\). The angle between the polarizer \(A\) and \(C\) is:
1. \(0^\circ\)
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

A system of three polarizers \(P_1,P_2,P_3\) is set up such that the pass axis of \(P_3\) is crossed with respect to that of \(P_1\). The pass axis of \(P_2\) is inclined at \(60^\circ\) to the pass axis of \(P_3\). When a beam of unpolarized light of intensity \(I_0\) is incident on \(P_1\), the intensity of light transmitted by the three polarizers is \(I\). The ratio (\(I_0/I\)) equals (nearly):
1. \(10.67\)
2. \(5.33\)
3. \(16.00\)
4. \(1.80\)

A beam of plane polarised light of large cross-sectional area and uniform intensity of \(3.3\) Wm^–2 falls normally on a polariser (cross-sectional area \(3 \times 10^{-4}~\text{m}^2\)) which rotates about its axis with an angular speed of \(31.4\) rad/s. The energy of light passing through the polariser per revolution, is close to:
1. \( 1.5 \times 10^{-4} ~\text{J} \)
2. \(1.0 \times 10^{-4} ~\text{J} \)
3. \( 5.0 \times 10^{-4} ~\text{J } \)
4. \( 1.0 \times 10^{-5} ~\text{J}\)

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as \(100\) Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by \(30^\circ\) in clockwise direction, the intensity of emerging light will be:
1. \(25~\text{Lumens}\)
2. \(50~\text{Lumens}\)
3. \(75~\text{Lumens}\)
4. \(100~\text{Lumens}\)