$A$ 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?

$A$ diverging beam of light from a point source $S$ having divergence angle $\alpha$,falls symmetrically on a glass slab as shown. The angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is $t$ and the refractive index is $n$,then the divergence angle of the emergent beam is

The observer at $O$ views two closely spaced spots on a vertical wall through an angled glass slab as shown. As seen by the observer,the spots appear

Light travels through a glass plate of thickness $t$ and having refractive index $\mu$. If $c$ is the velocity of light in vacuum, the time taken by the light to travel through this thickness of glass 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:

$A$ bubble in a glass slab (refractive index $1.5$) when viewed from one side appears at $5 \,cm$ and at $2 \,cm$ from the other side. Then the thickness of the slab is: (in $\,cm$)