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

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:

When a light ray enters from medium $i$ to medium $j$,if $_i\mu_j$ represents the refractive index,what is the product of $_2\mu_1 \times _3\mu_2 \times _4\mu_3$?

The frequency of a light ray is $6 \times 10^{14} \,Hz$. Its frequency when it propagates in a medium of refractive index $1.5$, will be

Light travels through a glass plate of thickness $t$ and having refractive index $n$. If $c$ is the velocity of light in vacuum,the time taken by the light to travel this thickness of glass is

$(a)$ The refractive index of glass is $1.5$. What is the speed of light in glass? (Speed of light in vacuum is $3.0 \times 10^{8} \; m/s$).
$(b)$ Is the speed of light in glass independent of the colour of light? If not,which of the two colours,red or violet,travels slower in a glass prism?