The velocity of light in glass,whose refractive index with respect to air is $1.5$,is $2 \times 10^8 \ m/s$. In a certain liquid,the velocity of light is found to be $2.5 \times 10^8 \ m/s$. The refractive index of the liquid with respect to air is:

$A$ beam of monochromatic blue light of wavelength $4200 Å$ in air travels in water of refractive index $4/3$. Its wavelength in water will be: (in $Å$)

The refractive index of air with respect to vacuum is . . . . . . .

Let the $x-z$ plane be the boundary between two transparent media. Medium $1$ in $z \ge 0$ has a refractive index of $\sqrt{2}$ and medium $2$ with $z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light in medium $1$ given by the vector $\overrightarrow{A} = 6\sqrt{3} \widehat{i} + 8\sqrt{3} \widehat{j} - 10\widehat{k}$ is incident on the plane of separation. The angle of refraction in medium $2$ is ......$^o$.

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

$A$ ray of light passes from vacuum into a medium of refractive index $n$. If the angle of incidence is twice the angle of refraction,then the angle of incidence in terms of refractive index is