$A$ monochromatic ray of light travels through a glass slab and a water column. The number of waves in a glass slab of thickness $4 \ cm$ is the same as in a water column of height $5 \ cm$. If the refractive index of glass is $\frac{5}{3}$,then the refractive index of water is:

Up to what height should we fill a glass of $21\, cm$ height so that it may appear half-filled? (Assume the refractive index of the liquid is $\mu = 1.5$)

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: $\mu_{water} = 4/3$)

$A$ point object is placed at a distance of $25 \, cm$ from a convex lens of focal length $20 \, cm$. If a glass slab of thickness $t$ and refractive index $1.5$ is inserted between the lens and the object,the image is formed at infinity. The thickness $t$ is....$cm$.

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

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: