The bottom of a container is a glass slab of thickness $4 \ cm$ and refractive index $\mu = 1.5$. The container contains two immiscible liquids $A$ and $B$ of depths $6 \ cm$ and $8 \ cm$ respectively. When a crack at the bottom surface of the glass slab is viewed from above,by what distance (in $cm$) does it appear to be shifted? The refractive indices of $A$ and $B$ are $1.4$ and $1.3$ respectively.

The back surface of a glass slab (refractive index $n$ and thickness $t$) is polished to act as a mirror,as shown in the figure. $A$ laser beam is incident on it,which is partially reflected and partially refracted at the air-glass interface. The refracted part is fully reflected at the mirror surface. $A$ pattern of discrete spots of light is observed on a screen placed perpendicular to the glass surface. The spacing between the spots on the screen is:

The apparent depth of a needle lying at the bottom of a tank,which is filled with water of refractive index $1.33$ to a height of $12.5\,cm$,is measured by a microscope to be $9.4\,cm$. If water is replaced by a liquid of refractive index $1.5$ up to the same height,what distance would the microscope have to be moved to focus on the needle again (in $,cm$)?

An air bubble in a glass slab $(\mu = 1.5)$ is $5 \, cm$ deep when viewed from one face and $2 \, cm$ deep when viewed from the opposite face. The thickness of the slab 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 of light 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 $cm$)

$A$ 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