The refractive index of the material of a crystal is $1.68$ and that of castor oil is $1.2$. When a ray of light passes from oil to the crystal,its velocity will change by a factor of:

Light of wavelength $7200 \ \mathring{A}$ in air. It has a wavelength in glass $(\mu = 1.5)$ equal to.......$\mathring{A}$

Light takes $8$ min $20$ sec to reach the Earth from the Sun. If the whole atmosphere were filled with water,how much time would the light take to reach the Earth? (Given refractive index of water,$_a\mu_w = 4/3$)

$A$ vessel of height $2d$ is half-filled with a liquid of refractive index $\sqrt{2}$ and the other half with a liquid of refractive index $n$ (the given liquids are immiscible). Then the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be

$A$ tank is filled with water to a height of $12.5 \, cm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \, cm$. If water is replaced by a liquid of refractive index $1.63$ up to the same height,what will be the apparent depth of the needle in $cm$?

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: