$A$ concave mirror is placed over a beaker containing water of refractive index $\mu = 1.33$. The object is placed at the bottom of the beaker. If the image of the object is formed at a distance of $25 \, cm$ from the top surface of the water,and the mirror is at a height of $15 \, cm$ above the water surface,find the focal length of the mirror in $cm$.

Time taken by the sunlight to pass through a window of thickness $4 \, mm$ whose refractive index is $1.5$ is

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

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:

$A$ 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:

$A$ vessel of depth $2d \ cm$ is half filled with a liquid of refractive index $\mu_1$ and the upper half with a liquid of refractive index $\mu_2$. The apparent depth of the vessel seen perpendicularly is