An air bubble in a glass slab with refractive index $1.5$ (near normal incidence) is $5\, cm$ deep when viewed from one surface and $3\, cm$ deep when viewed from the opposite face. The thickness (in $cm$) of the slab is

$A$ coin is placed at the bottom of a glass slab of refractive index $3$ and thickness $x$. Another glass slab of refractive index $\mu$ and thickness $x$ is placed on top of it. If the coin appears to be at the interface of the two slabs,then $\mu = $ . . . . . .

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

$A$ plane glass plate is placed over various coloured letters (violet,green,yellow,red). Which letter appears to be raised the most?

Three immiscible transparent liquids with uniform refractive indices $\frac{3}{2}, \frac{4}{3}$ and $\frac{6}{5}$ are arranged one on top of another. The depths of the liquids are $3 \ cm, 4 \ cm$ and $6 \ cm$ respectively. The apparent depth of the vessel is (in $cm$)

Each quarter of a vessel of depth $H$ is filled with liquids of the refractive indices $n_1, n_2, n_3$ and $n_4$ from the bottom respectively. The apparent depth of the vessel when looked normally is