The refractive index of air is $1.0003$. The thickness of an air column that will contain one more wavelength of yellow light $(6000 \mathring A)$ than in the same thickness in a vacuum is:

The optical path of a particular ray of light that has travelled a distance of $3 \ cm$ in flint glass is the same as that of a ray travelling a distance of '$x$' $cm$ through another medium. The value of '$x$' is [refractive index of flint glass $= 1.6$, refractive index of another medium $= 1.25$]. (in $cm$)

The optical path of a monochromatic light is the same if it goes through $4.0 \, cm$ of glass or $4.5 \, cm$ of water. If the refractive index of glass is $1.53$,the refractive index of water is:

$A$,$B$ and $C$ are parallel-sided transparent media of refractive indices $n_{1}$,$n_{2}$ and $n_{3}$ respectively. They are arranged as shown in the figure. $A$ ray is incident at an angle $i$ on the surface of separation of $A$ and $B$. After refraction into medium $B$,the ray grazes the surface of separation of media $B$ and $C$. Then,$\sin i$ equals to

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,$\sin i_c = \frac{1}{2}$

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