Polarization

‘$n$’ polarizing sheets are arranged such that each makes an angle $45°$ with the proceeding sheet. An unpolarized light of intensity $I$ is incident into this arrangement. The output intensity is found to be $\frac{I}{64}$ . The value of $n$ will be:

Two polaroids $A \text{and} B$ are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid $C$ is placed between $A \text{and} B$ bisecting angle between them. If intensity of unpolarised light is $I_0$ then intensity of transmitted light after passing through polaroid $B$ will be :

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are $2.8$ (medium –$1$) and $6.8$ (medium – $2$), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be ${\tan }^{-1}{\left(1+\frac{10}{\theta }\right)}^{\frac{1}{2}}$, the value of $\theta$ is ______.

(Given for dielectric media, ${\mu }_r=1$)

As shown in figures, three identical polaroids $P_1$, $P_2$ and $P_3$ are placed one after another. The pass axis of $P_2$ and $P_3$ are inclined at angle of $60º$ and $90º$ with respect to axis of $P_1$. The source $S$ has an intensity of $256 \mathrm{W} {\mathrm{m}}^{-2}$. The intensity of light at point $O$ is _____$\mathrm{W} {\mathrm{m}}^{-2}$.

Given below are two statements :
Statement I : If the Brewster's angle for the light propagating from air to glass is ${\theta }_B$, then Brewster's angle for the light propagating from glass to air is $\frac{\pi }{2}-{\theta }_B$.

Statement II : The Brewster's angle for the light propagating from glass to air is ${\tan }^{-1}\left({\mu }_{\mathrm{g}}\right)$, where ${\mu }_{\mathrm{g}}$ is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below :

An unpolarised light beam of intensity $2I_0$ is passed through a polaroid $P$ and then through another polaroid $Q$ which is oriented in such a way that its passing axis makes an angle of $30°$ relative to that of $P$. The intensity of the emergent light is

A wave of frequency $=3 \mathrm{GHz}$, strikes a particle of size ${\left(\frac{1}{100}\right)}^{th}$ of $\lambda$, then this phenomenon is called as

A source of light is placed in front of a screen. The intensity of light on the screen is $I$. Two Polaroids $P_1$ and $P_2$ are so placed in between the source of light and screen that the intensity of light on the screen is $\frac{I}{2}$. Then the $P_2$, should be rotated by an angle of (degrees) so that the intensity of light on the screen becomes $\frac{3I}{8}$.

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 $30°$ in clockwise direction, the intensity of emerging light will be _______Lumens.

A beam of plane polarized light of large cross-sectional area and uniform intensity of $3.3 \mathrm{W} {\mathrm{m}}^{–2}$ falls normally on a polarizer (cross-sectional area $3\times {10}^{–4} {\mathrm{m}}^2$), which rotates about its axis with an angular speed of $31.4 \mathrm{rad} {\mathrm{s}}^{-1}$. The energy of light passing through the polarizer per revolution, is close to:

$$\begin{gathered} In a Young\text{'}s double slit experiment, three \\ polarizers are kept as shown in the figure. \\ The transmission axes of P_1 and P_2 are orthogonal to \\ each other. The polarizer P_3 covers both the slits with its \\ transmission axis at 45° to those of P_1 and P_2. An unpolarized \\ light of wavelength \lambda and intensity I_0, is incident on P_1, and P_2. The \\ intensity at a point after P_3 where the path difference \\ \lambda between the light waves from s_1 and s_2 is \frac{\lambda }{3}, is \end{gathered}$$

A beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45°$ relative to that of $A$. The intensity of emergent light is :

When unpolarized light is incident at an angle of $60°$ on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :

A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just $10\%$ of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser needs to be rotated further, to reduce the output intensity to zero, is

A system of three polarizers ${\mathrm{P}}_1,{\mathrm{P}}_2,{\mathrm{P}}_3$ is set up such that the pass axis of ${\mathrm{P}}_3$ is crossed with respect to that of ${\mathrm{P}}_1$ . The pass axis of ${\mathrm{P}}_2$ is inclined at ${60}^{\mathrm{o}}$ to the pass axis of ${\mathrm{P}}_3.$ When a beam of unpolarized light of intensity ${\mathrm{I}}_{\mathrm{o}}$ is incident on ${\mathrm{P}}_1,$ the intensity of light transmitted by the three polarizers is $\mathrm{I}$ . The ratio $\left({\mathrm{I}}_{\mathrm{o}}/\mathrm{I}\right)$ equals (nearly):

Unpolarized light of intensity $I$ is incident on a system of two polarizers, $A$ followed by $B$. The intensity of emergent light is $\frac{I}{2}$ . If a third the polarizer $C$ is placed between $A$ and $B$ the intensity of emergent light is reduced to $\frac{I}{3}$ . The angle between the polarizers $A$ and $C$ is $\theta$ , then

Unpolarized light of intensity $\mathit{I}$ passes through an ideal polariser $A$. Another identical polariser $B$ is placed behind $A$. The intensity of light beyond B is found to be $\frac{\mathit{I}}{2}$. Now another identical polariser $C$ is placed between $A$ and $B$. The intensity beyond B is now found to be $\frac{\mathit{I}}{8}$ . The angle between polariser $A$ and $C$ is

Unpolarized light of intensity $I_0$ is incident on surface of a block of glass at Brewster's angle. In that case, which one of the following statements is true?

Two beams, A and B of plane polarized light with mutually perpendicular planes of polarization are seen through a polaroid. From the position when the beam A has maximum intensity (and beam B has zero intensity), a rotation of polaroid through 30^o makes the two beams appear equally bright. If the initial intensities of the two beams are I_A and I_B respectively, then $\frac{{\text{I}}_{\text{A}}}{{\text{I}}_{\text{B}}}$ equals :