$A$ microscope is focused on a mark on a piece of paper and then a slab of glass of thickness $3\, cm$ and refractive index $1.5$ is placed over the mark. How should the microscope be moved to get the mark in focus again?

Mention the relation between the real depth and the apparent depth in terms of the refractive indices of the media.

Consider three media $P$, $Q$, and $R$ with refractive indices $1$, $1.25$, and $1.5$, respectively. The medium $Q$ having a thickness of $5 \text{ cm}$ is placed between extended media $P$ and $R$. An object $O$ is placed at the centre of medium $Q$. If viewed from medium $P$ near the normal direction, the apparent depth of $O$ is $h_1$. For similar observation from medium $R$, the apparent depth is $h_2$. The value of $|h_1 - h_2|$, in $\text{cm}$, is:

$A$ vessel of depth $d$ is half filled with oil of refractive index $n_1$ and the other half is filled with water of refractive index $n_2$. The apparent depth of this vessel when viewed from above 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 $6 \ cm$ is the same as in a water column of height $7 \ cm$. If the refractive index of glass is $1.5$,then the refractive index of water is:

$A$ paraxial beam of light is converging towards a point $P$ on the screen. $A$ plane parallel sheet of glass of thickness $t$ and refractive index $\mu$ is introduced in the path of the beam. The convergence point is shifted by: