$A$ cubical vessel has opaque walls. An observer is located such that she can see only the wall $CD$,but not the bottom. To what height (in $cm$) should water be poured so that she can see an object placed at the bottom at a distance of $10 \, cm$ from the corner $C$? The refractive index of water is $\mu = 1.33 \approx 4/3$.

Monochromatic light of frequency $5 \times 10^{14} \ Hz$ travelling in vacuum enters a medium of refractive index $1.5$. Its wavelength in the medium is ....... $\mathring{A}$.

Light enters from air into a given medium at an angle of $45^{\circ}$ with the interface of the air-medium surface. After refraction,the light ray is deviated through an angle of $15^{\circ}$ from its original direction. The refractive index of the medium 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 $m$?

When a light ray is incident on a medium at an angle $i$ and refracted into a second medium at an angle $r$,the graph of $\sin r$ vs $\sin i$ is as shown below. From this,one can conclude that:
$(A)$ Velocity of light in the second medium is $1.73$ times the velocity of light in the first medium
$(B)$ Velocity of light in the first medium is $1.73$ times the velocity in the second medium
$(C)$ The critical angle for the two media is given by,$\sin i_c = \frac{1}{\sqrt{3}}$
$(D)$ The critical angle for the two media is given by,$\sin i_c = \frac{1}{2}$

$A$ ray of light is incident at the glass-water interface at an angle $i$. It emerges finally parallel to the surface of water. The value of ${\mu _g}$ is (given refractive index of water ${\mu _w} = 4/3$):