Refraction at plane surfaces

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:

Light ray incident along a vector $\overrightarrow{AO}$ $\left(\overrightarrow{AO}=2\hat i-3\hat j\right)$ emerges out along vector $\overrightarrow{OB}$ $\left(\overrightarrow{OB}=C\hat i-4\hat j\right)$ as shown in the figure below. The value of C is ________.

Two identical concave mirrors each of focal length $f$ are facing each other as shown in the schematic diagram. The focal length $f$ is much larger than the size of the mirrors. A glass slab of thickness $t$ and refractive index $n_0$ is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source $S$ is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on $S$ itself, which of the following distances between the two mirrors is/are correct:

A light ray is incident on the surface of a sphere of refractive index $n$ at an angle of incidence $\theta_0$. The ray partially refracts into the sphere with angle of refraction $\phi_0$ and then partly reflects from the back surface. The reflected ray then emerges out of the sphere after a partial refraction. The total angle of deviation of the emergent ray with respect to the incident ray is $\alpha$. Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

Two equilateral-triangular prisms P₁ and P₂ are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism P₁ at an angle of incidence $\theta$ such that the outgoing ray undergoes minimum deviation in prism P₂. If the respective refractive indices of P₁ and P₂ are $\sqrt{\dfrac32}$ and $\sqrt3$, then $\theta = \sin^{-1}\left[\sqrt{\dfrac32}\sin\left(\dfrac{\pi}{\beta}\right)\right]$, where the value of $\beta$ is _____.

A monochromatic light wave is incident normally on a glass slab of thickness $d$, as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height $h$. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

Consider a configuration of $n$ identical units, each consisting of three layers. The first layer is a column of air of height $h = \dfrac13$ cm, and the second and third layers are of equal thickness $d = \dfrac{\sqrt3 - 1}{2}$ cm, and refractive indices $\mu_1 = \sqrt{\dfrac32}$ and $\mu_2 = \sqrt3$, respectively. A light source O is placed on the top of the first unit, as shown in the figure. A ray of light from O is incident on the second layer of the first unit at an angle of $\theta = 60^\circ$ to the normal. For a specific value of $n$, the ray of light emerges from the bottom of the configuration at a distance $l = \dfrac{8}{\sqrt3}$ cm, as shown in the figure. The value of $n$ is _____.

A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_2$. The other slit is at the interface of this medium with another medium 1 of refractive index $n_1\ (\neq n_2)$. The line joining the slits is perpendicular to the interface and the distance between the slits is $d$. The slit widths are much smaller than $d$. A monochromatic parallel beam of light is incident on the slits from medium 1. A detector is placed in medium 2 at a large distance from the slits, and at an angle $\theta$ from the line joining them, so that $\theta$ equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.

Which of the following statement(s) is(are) correct?

A ray of light is incident at an angle of incidence 60° on the glass slab of refractive index $\sqrt3$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is $4\sqrt3$ cm. The thickness of the glass slab is ______ cm.

The difference of speed of light in the two media A and B $(v_A-v_B)$ is $2.6\times10^7$ m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is : (Given : speed of light in vacuum $c=3\times10^8\ \mathrm{ms^{-1}}$)

Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2n}$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

If a wave gets refracted into a denser medium, then which of the following is true?

Time taken by light to travel in two different materials A and B of refractive indices $\mu_A$ and $\mu_B$ of same thickness is $t_1$ and $t_2$ respectively. If $t_2-t_1=5\times10^{-10}$ s and the ratio of $\mu_A$ to $\mu_B$ is 1 : 2. Then, the thickness of material, in meter is : (Given $v_A$ and $v_B$ are velocities of light in A and B materials respectively.)

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm form the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screeen ?

The X-Y plane be taken as the boundary between two transparent media M$_1$ and M$_2$. M$_1$ in Z ⩾ 0 has a refractive index of $\sqrt2$ and M$_2$ with Z < 0 has a refractive index of $\sqrt3$. A ray of light travelling in M$_1$ along the direction given by the vector $\vec P=4\sqrt3\hat i-3\sqrt3\hat j-5\hat k$, is incident on the plane of separation. The value of difference between the angle of incident in M$_1$ and the angle of refraction in M$_2$ will be _______ degree.

Light enters from air into a given medium at an angle of 45° with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of 15° from its original direction. The refractive index of the medium is :

A ring is placed at the bottom of a trough containing four immiscible liquids of refractive indices 1.0, 2.0, 3.0 and 4.0 poured one above the other of heights 10 cm, 20 cm, 30 cm, and 40 cm respectively. The apparent depth at which the ring appears, when seen from outside is _______ cm.

A wide slab consisting of two media of refractive indices $n_1$ and $n_2$ is placed in air as shown in the figure. A ray of light is incident from medium $n_1$ to $n_2$ at an angle $\theta$, where $\sin\theta$ is slightly larger than $1/n_1$. Take refractive index of air as 1. Which of the following statement(s) is(are) correct?

For a prism of prism angle $\theta = 60^\circ$, the refractive indices of the left half and the right half are, respectively, $n_1$ and $n_2$ $(n_2 \ge n_1)$ as shown in the figure. The angle of incidence $i$ is chosen such that the incident light rays will have minimum deviation if $n_1 = n_2 = n = 1.5$. For the case of unequal refractive indices, $n_1 = n$ and $n_2 = n + \Delta n$ (where $\Delta n \ll n$), the angle of emergence $e = i + \Delta e$. Which of the following statement(s) is(are) correct?

A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale)