$AB$ is an object of length $l$ dipped in water at a depth of $d$. It is viewed from air at near-normal incidence. The length of the image is

$A$ layer of oil $3\,cm$ thick is floating on a layer of coloured water $5\,cm$ thick. The refractive index of coloured water is $5/3$ and the apparent depth of the two liquids appears to be $36/7\,cm$. Find the refractive index of oil.

$A$ paraxial beam is incident on a glass $(n = 1.5)$ hemisphere of radius $R = 6\, cm$ in air as shown. The distance of the point of convergence $F$ from the plane surface of the hemisphere is......$cm$.

$A$ glass slab of thickness $4 \ cm$ contains the same number of waves as $5 \ cm$ of water when both are traversed by the same monochromatic ray of light. The refractive index of water is $4/3$. What is the refractive index of glass?

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:

$A$ microscope is focused on a mark on a piece of paper and then a slab of glass of thickness $3\, cm$ and refractive index $1.5$ is placed over the mark. How should the microscope be moved to get the mark in focus again?