Refraction at Spherical Surfaces and by Lenses

There are certain material developed in laboratories which have a negative refractive index (Figure). A ray incident from air (medium $1$) into such a medium (medium $2$) shall follow a path given by

The optical density of turpentine is higher than that of water while its mass density is lower. Figure given below shows a layer of turpentine floating over water in a container. For which one of the four rays incident on turpentine in figure, the path shown is correct?

The radius of curvature of the curved surface of a plano-convex lens is $20 \mathrm{cm}$. If the refractive index of the material of the lens be $1.5$, it will

An object approaches a convergent lens from the left of the lens with a uniform speed $5 \mathrm{m}/\mathrm{s}$ and stops at the focus. The Image

A short pulse of white light is incident from air to a glass slab at normal incidence. After travelling through the slab, the first colour to emerge is

An infinitely long cylinder of radius $R$ is made of an unusual exotic material with refractive index –1 (Figure). The cylinder is placed between two planes whose normals are along the $y$ direction. The centre of the cylinder $\mathrm{O}$ lies along the $y$-axis. A narrow laser beam is directed along the $y$ direction from the lower plate. The laser source is at a horizontal distance $x$ from the diameter in the $y$ direction. Find the range of $x$ such that light emitted from the lower plane does not reach the upper plane.

If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by

$n\left(r\right)=1+2 GM/r{c}^2$

where $r$ is the distance of the point of consideration from the centre of the mass of the massive body, $G$ is the universal gravitational constant, $M$ the mass of the body and $c$ the speed of light in vacuum. Considering a spherical object find the deviation of the ray from the original path as it grazes the object.
 

The mixture of a pure liquid and a solution in a long vertical column (i.e, horizontal dimensions $<<$ vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical has deviated from its original path. Find the deviation in travelling a horizontal distance $d<<h$, the height of the column.

Show that for a material with refractive index $\mu \ge \sqrt{2}$ , light incident at any angle shall be guided along a length perpendicular to the incident face.

Three immiscible liquids of densities $d_1>d_2>d_3$ and refractive indices ${\mu }_1>{\mu }_2>{\mu }_3$ are put in a beaker. The height of each liquid column is $\frac{h}{3}$. A dot is made at the bottom of the beaker. For near normal vision, find the apparent depth of the dot.

An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is reversed?

A magnifying glass is used, as the object to be viewed can be brought closer to the eye than the normal near point. This results in

A rectangular block of glass $\mathrm{ABCD}$ has a refractive index $1.6$. A pin is placed midway on the face $\mathrm{AB}$ (Figure). When observed from the face $\mathrm{AD}$. the pin shall