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

$A$ vessel of depth $x$ is half filled with oil of refractive index $\mu_1$ and the other half is filled with water of refractive index $\mu_2$. The apparent depth of the vessel when viewed from above is

When a convex lens is placed above an empty tank, the image of a mark at the bottom of the tank, which is $45 \ cm$ from the lens, is formed $36 \ cm$ above the lens. When a liquid is poured in the tank to a depth of $40 \ cm$, the distance of the image of the mark above the lens is $48 \ cm$. The refractive index of the liquid is

To a bird in air, a fish in water appears to be at $30 \,cm$ from the surface. If the refractive index of water with respect to air is $\frac{4}{3}$, the real depth of the fish from the surface is: (in $\,cm$)

$A$ vessel of depth $2h$ is half-filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$. The liquids are immiscible. The apparent depth of the inner surface of the bottom of the vessel will be:

$A$ parallel-sided block of glass with a refractive index of $1.5$ and a thickness of $36 \, mm$ rests on the floor of a tank filled with water (refractive index $= 4/3$). The difference between the apparent depth of the floor at $A$ (where the glass block is present) and $B$ (where only water is present) when seen from vertically above is equal to $....... \, mm$.