When the same monochromatic ray of light travels through a glass slab and through water,the number of waves in a glass slab of thickness $5 \ cm$ is the same as in a water column of height $6 \ cm$. If the refractive index of glass is $1.56$,then the refractive index of water is:

Two transparent slabs have the same thickness $t$. One is made of material $X$ of refractive index $1.5$. The other is made of two materials $Y$ and $Z$ having thicknesses in the ratio $1 : 2$. The refractive index of $Z$ is $1.6$. If a monochromatic parallel beam passing through the slabs has the same number of wavelengths inside both,the refractive index of $Y$ 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

$A$ ray of light is incident on a surface of a glass slab at an angle of $45^{\circ}$. If the lateral shift produced per unit thickness is $\frac{1}{\sqrt{3}}$,the angle of refraction produced is

$A$ glass hemisphere of radius $0.04\, m$ and refractive index $1.6$ is placed centrally over a cross mark on a paper:
$(i)$ with the flat face in contact with the paper;
$(ii)$ with the curved face in contact with the paper.
In each case,the cross mark is viewed directly from above. The positions of the images will be:

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 $\,cm$)