$A$ 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?

$A$ 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:

One side of a glass slab is silvered as shown. $A$ ray of light is incident on the other side at an angle of incidence $i = 45^o$. The refractive index of the glass is $1.5$. The deviation of the ray of light from its initial path when it comes out of the slab is......$^o$.

$A$ ray of light is incident on a parallel slab of thickness $t$ and refractive index $n$. If the angle of incidence $\theta$ is small,then the lateral displacement between the incident and emergent ray will be

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:

$A$ transparent glass cube of length $24 \,cm$ has a small air bubble trapped inside. When seen normally through one surface from air outside, its apparent distance is $10 \,cm$ from the surface. When seen normally from the opposite surface, its apparent distance is $6 \,cm$. The distance of the air bubble from the first surface is (in $\,cm$)