$A$ glass slab of thickness $6.0 \text{ cm}$ is placed on a piece of paper on which an ink dot is marked. By how much distance would the ink dot appear to be raised (in $\text{ cm}$)? The velocity of light in glass is $2 \times 10^8 \text{ m/s}$ and that in air is $3 \times 10^8 \text{ m/s}$.

$A$ ray of light is incident on one face of a transparent slab of thickness $15 \, cm$. The angle of incidence is $60^{\circ}$. If the lateral displacement of the ray on emerging from the parallel plane is $5\sqrt{3} \, cm$,the refractive index of the material of the slab is:

When the same monochromatic ray of light travels through a glass slab and through water,the number of waves in a glass slab of thickness $5 \ cm$ is the same as in a water column of height $6 \ cm$. If the refractive index of glass is $1.56$,then the refractive index of water is:

$A$ beam of light composed of red and green rays is incident obliquely at a point on the face of a rectangular glass slab. When coming out on the opposite parallel face, the red and green rays emerge from

Consider the situation shown in the figure. Water $\left( \mu_w = \frac{4}{3} \right)$ is filled in a beaker up to a height of $10 \, cm$. $A$ plane mirror is fixed at a height of $5 \, cm$ from the surface of the water. The distance of the image from the mirror after reflection of an object $O$ at the bottom of the beaker is......$cm$.

$A$ ray of light is incident normally on a glass slab of thickness $5 \ cm$ and refractive index $1.6$. The time taken by a ray to travel from the source to the surface of the slab is the same as the time taken to travel through the glass slab. The distance of the source from the surface is: (in $cm$)