$A$ bird is flying at $12 \ m$ height above the water surface and a fish is swimming $16 \ m$ below the water surface $(\mu_{\text{water}} = 4/3)$. Find the distance of the bird with respect to the fish as seen by the fish. (in $m$)

$A$ 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

In finding out the refractive index of a glass slab,the following observations were made through a travelling microscope: $50$ vernier scale divisions $= 49$ $MSD$; $20$ divisions on the main scale in each $cm$. For a mark on paper:
$MSR = 8.45 \ cm, VC = 26$
For the mark on paper seen through the slab:
$MSR = 7.12 \ cm, VC = 41$
For a powder particle on the top surface of the glass slab:
$MSR = 4.05 \ cm, VC = 1$
($MSR =$ Main Scale Reading,$VC =$ Vernier Coincidence)
The refractive index of the glass slab is:

The ratio of the thickness of plates of two transparent mediums $A$ and $B$ is $6 : 4$. If light takes equal time in passing through them,then the refractive index of $B$ with respect to $A$ will be:

An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2I$,where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. As the beam enters the medium,it will:

If the velocity of light in the first medium is $v_1$ and in the second medium is $v_2$,then the refractive index of the second medium with respect to the first medium is given by: