Polarisation and Brewster's law

In the List-I, four optical effects are mentioned. The physical phenomena of light which are essential to describe these optical effects are given in List-II. Choose the option which describes the correct match between the entries in List-I to those in List-II.

As shown in the figure, a ray $AB$ of unpolarized light enters from water of refractive index $n_w=4/3$ into a medium of refractive index $n_p=4/\sqrt3$ after passing through a glass plate of refractive index $n_g=1.5$ and a layer of water. At a particular incident angle $i$ the reflected ray $CD$ is polarized in the direction as shown in the figure. The value of $i$ (in degrees) is:

An unpolarized light is incident on the plane interface of air-dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at 30° and 90°, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at 60° with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is ________.

An unpolarized light of intensity $I_o$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is 0° and intensity of light emerged from analyser is $\dfrac38I_o$, the angle of rotation of the light by the solution with respect to analyser is ________ degrees.

A solid glass sphere of refractive index $n = \sqrt3$ and radius $R$ contains a spherical air cavity of radius $\dfrac{R}{2}$, as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index $n = 1$) remains inside the glass sphere. An unpolarized, unidirectional and monochromatic light source $S$ emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point O and is fully polarized, then the angle of incidence at the inner surface of the glass sphere is $\theta$. The value of $\sin\theta$ is _____.

A point source S emits unpolarized light uniformly in all directions. At two points A and B, the ratio $r = I_A/I_B$ of the intensities of light is 2. If a set of two polaroids having $45^{\circ}$ angle between their pass-axes is placed just before point B, then the new value of $r$ will be _____.

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $\delta = 60^\circ$ (see Figure-1). The angle of minimum deviation for red light from the same prism is $\delta_{\min} = 30^\circ$ (see Figure-2). The refractive index of the prism material for blue light is $\sqrt3$. Which of the following statement(s) is(are) correct?

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec E = 30(2\hat x + \hat y)\sin\left[2\pi\left(5\times10^{14}\,t - \frac{10^7}{3}z\right)\right]\ \mathrm{V\,m^{-1}}$. Which of the following option(s) is(are) correct?

[Given: The speed of light in vacuum, $c = 3\times10^8\ \mathrm{m\,s^{-1}}$]

A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

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

Two poloroids P$_1$ and P$_2$ are placed parallel to each other with common axis. The light of intensity I$_0$ passes through a polaroid sheet P$_1$ and then passes through polaroid P$_2$. If P$_2$ is now rotated by 60°, then the intensity of the output light from P$_2$ will be:

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.

Let the refractive index of a denser medium with respect to a rarer medium be $n_{12}$ and its critical angle be $\theta_C$. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90°. Angle A is given by :

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° 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 :

A ray of light is incident from a denser to a rarer medium. The critical angle for total internal reflection is $\theta_{iC}$ and the Brewster's angle of incidence is $\theta_{iB}$, such that $\sin\theta_{iC}/\sin\theta_{iB}=\eta=1.28$. The relative refractive index of the two media is :