$A$ printed page is pressed by a glass of water. The refractive index of the glass and water is $1.5$ and $1.33$,respectively. If the thickness of the bottom of the glass is $1\, cm$ and the depth of the water is $5\, cm$,how much will the page appear to be shifted if viewed from the top (in $,cm$)?

An object is placed $20 \ cm$ in front of a $4 \ cm$ thick plane mirror. The image of the object is finally formed at $45 \ cm$ from the object itself. The refractive index of the material of the unpolished side of the mirror is (considering near normal incidence):

$A$ 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 $cm$.

If the velocity of light in vacuum is $3 \times 10^{8} \text{ m/s}$,the time taken (in nanoseconds) to travel through a glass plate of thickness $10 \text{ cm}$ and refractive index $1.5$ is:

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

Three immiscible transparent liquids with refractive indices $3/2, 4/3$ and $6/5$ are arranged one above the other in a container. The depths of the liquids are $3 \text{ cm}, 4 \text{ cm}$ and $6 \text{ cm}$ respectively. The apparent depth of the vessel is (in $\text{ cm}$)