What is difference between ray of light and beam of light?

The radii of curvature of the faces of a double convex lens made of glass, are $10 \mathrm{cm}$ and $15 \mathrm{cm}$. Its focal length is $12 \mathrm{cm}$.

$\left(\mathrm{a}\right)$ Find the refractive index of glass

$\left(\mathrm{b}\right)$ Calculate its new focal length if the lens is completely immersed in water ( Refractive index of water is $\frac{4}{3}$)

In a medium the speed of light wave decreases to $0.2$ times to its speed in free space. The ratio of relative permittivity to the refractive index of the medium is $x:1$. The value of $x$ is ______.

(Given speed of light in free space $=3\times {10}^8 \mathrm{m} {\mathrm{s}}^{-1}$ and for the given medium ${\mu }_r=1$)

The following graph depicts the inverse of magnification versus the distance between the object and lens data for a setup. The focal length of the lens used in the setup is

Distance between the object and the lens $\left(\mathrm{m}\right)$

A monochromatic light source $S$, is placed between a mirror and a screen as shown in the figure below,

Remote objects are viewed through a converging lens with a focal length $F=9 \mathrm{cm}$ placed at a distance $a=36 \mathrm{cm}$ in front of the eye.

Estimate the minimum size of the screen that should be placed behind the lens so that the entire field of view is covered. Where should the screen be placed? Assume that the radius $r$ of the pupil is approximately $1.5 \mathrm{mm}$.

A cylindrical transparent vessel of height $h\left(h\ll R_{\mathrm{ves}}\right)$, where $R_{\mathrm{ves}}$ is the radius of the vessel, is filled with an ideal gas of molar mass $\mu$ at a temperature $T$ and a pressure $p_0$. The dependence of the refractive index $n$ of the gas on its density $\rho$ obeys the law $n=1+\alpha \rho$. The vessel is rotated at an angular velocity $\omega$ about its axis. A narrow parallel beam of light of radius $r_{\mathrm{beam}}$ is incident along the axis of the vessel.

Determine the radius $R$ of the spot on the screen placed at right angles to the vessel axis at a distance $L$ behind the vessel, assuming that the change in the gas pressure at each point of the vessel due to rotation is small as compared with $p_0$. The effect of the end faces of the vessel on the path of the rays should be neglected.

The beam from an argon laser (of wavelength $515 \mathrm{nm}$) has a diameter $d$ of $3.00 \mathrm{mm}$ and a continuous energy output rate of $4.00 \mathrm{W}.$ The beam is focused onto a diffuse surface by a lens whose focal length $f$ is $3.50 \mathrm{cm}.$ A diffraction pattern is formed, the radius of the central disk being given by $R=\frac{1.22f\mathrm{\lambda }}{d}$. The central disk can be shown to contain $84\%$ of the incident power. $\left(\mathrm{a}\right)$ What is the radius of the central disk? $\left(\mathrm{b}\right)$ What is the average intensity (power per unit area) in the incident beam? $\left(\mathrm{c}\right)$ What is the average intensity in the central disk?