STATEMENT-$1$: A thin white parallel beam of light is incident on a plane glass-vacuum interface as shown. The beam may not undergo dispersion after suffering deviation at the interface (The beam is not incident normally on the interface.)

STATEMENT-$2$: Vacuum has the same refractive index for all colours of white light.

In cases of real images formed by a thin convex lens, the linear magnification is

$\left(\mathrm{I}\right)$ directly proportional to the image distance,

$\left(\mathrm{II}\right)$ inversely proportional to the object distance,

$\left(\mathrm{III}\right)$ directly proportional to the distance of image from the nearest principal focus,

$\left(\mathrm{IV}\right)$ inversely proportional to the distance of the object from the nearest principal focus.

From these, the correct statements are,

Rays from an object immersed in water $\left(\mu =1.33\right)$ traverse a spherical air bubble of radius $R$. If the object is located far away from the bubble, its image as seen by the observer located on the other side of the bubble will be

A light ray $I$ is an incident on a plane mirror $M$. The mirror is rotated in the direction as shown in the figure by an arrow at frequency $9/\mathrm{\pi } \mathrm{rps}$. The light reflected by the mirror is received on the wall $W$ at a distance $10 \mathrm{m}$ from the axis of rotation. When the angle of incidence becomes $37°$ the speed of the spot (a point) on the wall is $v\times {10}^2 \mathrm{m} {\mathrm{s}}^{-1}$. Find the value of $v$.

A convex mirror and a concave mirror each of focal length $10 \mathrm{cm}$ are placed coaxially. They are separated by $40 \mathrm{cm}$ and their reflecting surfaces face each other. A point object is kept on the principal axis at a distance $x \mathrm{cm}$ from the concave mirror such that the final image after two reflections, first on the concave mirror, is on the object itself. Write the value of $x$ to the nearest integer.

A point object is placed on the principal axis of a concave mirror of radius of curvature $20 \mathrm{cm}$ at a distance $31 \mathrm{cm}$ from the pole of the mirror. A glass slab of thickness $3 \mathrm{cm}$ and refractive index $1.5$ is placed between object and mirror as shown in the figure.

Find the distance $\left(\text{in} \mathrm{cm}\right)$ of the final image formed by the system from the mirror.

Light is incident from glass to air. The variation of the angle of deviation $\delta$ with the angle of incidence $i$ for $0<i<90°$ is shown. The refractive index of glass is $\frac{2}{\sqrt{3}}$. If the value of $\left(x+y+z\right)$ is $\frac{n\mathrm{\pi }}{6}$, then find the value of $n$.