$A$ ray of light falls on a transparent glass slab with a refractive index (relative to air) of $1.62$. The angle of incidence for which the reflected and refracted rays are mutually perpendicular is

$A$ monochromatic light is travelling in a medium of refractive index $n=1.6$. It enters a stack of glass layers from the bottom side at an angle $\theta=30^{\circ}$. The interfaces of the glass layers are parallel to each other. The refractive indices of different glass layers are monotonically decreasing as $n_m=n-m \Delta n$,where $n_m$ is the refractive index of the $m^{\text{th}}$ slab and $\Delta n=0.1$ (see the figure). The ray is refracted out parallel to the interface between the $(m-1)^{\text{th}}$ and $m^{\text{th}}$ slabs from the right side of the stack. What is the value of $m$?

The apparent depth of water in a cylindrical water tank of diameter $2R \ cm$ is reducing at the rate of $x \ cm/minute$ when water is being drained out at a constant rate. The amount of water drained in $c.c./minute$ is: ($n_1 =$ refractive index of air,$n_2 =$ refractive index of water)

When an object is moved along the principal axis of a concave mirror placed in air,the image coincides with the object if the object is $50 \ cm$ from the mirror. If the mirror is placed at a depth of $20 \ cm$ in a transparent medium,the image coincides with the object when the object is $40 \ cm$ from the mirror. The refractive index of the liquid is

In the figure given below,a ray of light travelling in a medium of refractive index $\mu$ passes through two different connected rectangular blocks of refractive indices $\mu_1$ and $\mu_2$ $(\mu_2 > \mu_1)$. The angle of incidence $\theta_1$ is increased slightly. Then,the angle $\theta_2$ is

What are optically denser and optically rarer media?