$A$ 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?

$A$ monochromatic ray of light travels through a glass slab and a water column. The number of waves in a glass slab of thickness $4 \,cm$ is the same as in a water column of height $5 \,cm$. If the refractive index of glass is $\frac{5}{3}$, then the refractive index of water is:

$A$ microscope is focused on a point object and then its objective is raised through a height of $2 \ cm$. If a glass slab of refractive index $1.5$ is placed over this point object such that it is focused again,the thickness of the glass slab is......$cm$

$A$ 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......$cm$.

Two transparent slabs have the same thickness as shown. One is made of material $A$ of refractive index $1.5$. The other is made of two materials $B$ and $C$ with thickness in the ratio $1 : 2$. The refractive index of $C$ is $1.6$. If a monochromatic parallel beam passing through the slabs has the same number of waves inside both,the refractive index of $B$ is

$A$ transparent cube of $15\, cm$ edge contains a small air bubble. Its apparent depth when viewed through one face is $6\, cm$ and when viewed through the opposite face is $4\, cm$. Then the refractive index of the material of the cube is