$A$ travelling microscope is focused on an ink dot marked on a glass slab $(\mu = 1.5)$ of thickness $0.12 \,m$. By what distance should the microscope be moved to focus on the ink dot again after the slab is placed?

$A$ 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:

What is the time taken (in seconds) for light to cross a glass slab of thickness $4 \ mm$ and refractive index $\mu = 3$?

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness $h$ in terms of the angle of incidence $i$ and angle of refraction $r$,if the glass slab is placed in air medium?

$A$ 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 $\,cm$)

$A$ flat glass slab of thickness $6\, cm$ and refractive index $1.5$ is placed in front of a plane mirror. An observer is standing behind the glass slab and looking at the mirror. The actual distance of the observer from the mirror is $50\, cm$. The distance of his image from himself,as seen by the observer is .......$cm$.