An air bubble in a glass slab $(\mu = 1.5)$ appears to be $5 \, cm$ deep when viewed through one face and $2 \, cm$ deep when viewed through the opposite face. What is the thickness of the slab in $cm$?

The time required for light to pass through a glass slab of $2 \ mm$ thickness is $({\mu _{glass}} = 1.5)$.

The figure shows a ray of light entering and passing through a dense glass slab and emerging from the other side. If the angle of incidence $i=60^{\circ}$, slab thickness $b=0.04 \text{ m}$, and the refractive index of glass $\mu=\sqrt{3}$, the parallel shift $d$ between the emerging and entering rays in $\text{mm}$ is:

In a vessel of $21 \, cm$ depth,up to what height should water be filled so that it appears to be $20\%$ filled when viewed from the top (in $, cm$)? (Given: $\mu_{water} = 4/3$)

$A$ vessel is filled with two different liquids which do not mix. One liquid is $40 \ cm$ deep with a refractive index of $1.6$,and the other is $30 \ cm$ deep with a refractive index of $1.5$. What is the apparent depth of the vessel when viewed normally (in $cm$)?

An object lying $100 \ cm$ inside water is viewed normally from air. If the refractive index of water is $\frac{4}{3}$,then the apparent depth of the object is (in $cm$)