A plane-polarized light with intensity \(I_0\) is incident on a polaroid with an electric field vector making an angle of \(60^{\circ}\) with the transmission axis of the polaroid. The intensity of the resulting light will be:
1. \(\frac{I_0}{4}\)
2. \(I_0\)
3. \(2I_0\)
4. \(\frac{I_0}{2}\)

Which of the following statements indicates that light waves are transverse? 

Five identical polaroids are placed coaxially with \(45^{\circ}\) angular separation between pass axes of adjacent polaroids as shown in the figure. (I₀: Intensity of unpolarized light)
          
The intensity of light, I, emerging out of the 5^th polaroid is:

1.  $\frac{{\mathrm{I}}_0}{4}$

2.  $\frac{{\mathrm{I}}_0}{8}$

3.  $\frac{{\mathrm{I}}_0}{16}$

4.  $\frac{{\mathrm{I}}_0}{32}$

Two polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light of intensity I_o is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its axis makes an angle 45° with that of P₁. The intensity of transmitted light through P₂ is:

1. $\frac{I_0}{4}$

2. $\frac{I_0}{8}$

3. $\frac{I_0}{16}$

4. $\frac{I_0}{2}$

When an unpolarized light of intensity I₀ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is:

1. Zero

2. I₀

3. $\frac{1}{2}{I}_0$

4. $\frac{1}{4}{I}_0$

Two polaroids are kept crossed to each other. Now one of them is rotated through an angle of $45°$. The percentage of incident light now transmitted through the system is:

1.  15%

2.  25%

3.  50%

4.  60%

A beam of unpolarized light of intensity $I_0$ is passed first through a tourmaline crystal A and then through another tourmaline crystal B oriented so that its principal plane is parallel to that of A. The intensity of the final emergent light is I. The value of I is:

1.  $I_0$

2.  $\frac{I_0}{2}$

3.  $\frac{I_0}{4}$

4.  $\frac{I_0}{8}$

Unpolarized light of intensity 32 Wm^–2 passes through three polarizers such that the transmission axes of the first and second polarizer make an angle of 30° with each other and the transmission axis of the last polarizer is crossed with that of the first. The intensity of the final emerging light will be:

1. 32 Wm^–2

2. 3 Wm^–2

3. 8 Wm^–2

4. 4 Wm^–2

Two polaroids are in the path of an unpolarized beam of intensity ${\mathrm{I}}_0$ such that no light is emitted from the second polaroid. If a third polaroid, whose polarization axis makes an angle $\mathrm{\theta }$ with the polarization axis of the first polaroid, is placed between these polaroids, then the intensity of light emerging from the last polaroid will be:

1. \(\left ( \frac{I_{0}}{8} \right )\sin^{2}2\theta \)
2. \(\left ( \frac{I_{0}}{4} \right )\sin^{2}2\theta \)
3. \(\left ( \frac{I_{0}}{2} \right )\sin^{4}2\theta \)
4. \(I_{0}\sin^{2}2\theta \)

An unpolarised light incident on a polariser has amplitude A, and the angle between analyzer and polariser is \(60^{\circ}\). The light transmitted by the analyzer has an amplitude of:

1. $A\sqrt{2}$

2. $A/2\sqrt{2}$

3. $\sqrt{3}A/2$

4. A/2