An empty tank has a concave mirror at its bottom. When sunlight falls normally on the mirror, it is focused at a height of $32 \,cm$ from the mirror. If the tank is filled with water up to a height of $20 \,cm$, then the sunlight focuses at (refractive index of water $= 4/3$):

$A$ beaker containing liquid is placed on a table,underneath a microscope which can be moved along a vertical scale. The microscope is focused,through the liquid,onto a mark on the table when the reading on the scale is $a$. It is next focused on the upper surface of the liquid and the reading is $b$. More liquid is added and the observations are repeated,the corresponding readings are $c$ and $d$. The refractive index of the liquid is

$A$ convex lens is placed $10\, cm$ from a light source and it forms a sharp image on a screen,kept $10\, cm$ from the lens. Now,a glass block (refractive index $\mu = 1.5$) of $1.5\, cm$ thickness is placed in contact with the light source. To get the sharp image again,the screen is shifted by a distance $d$. Then $d$ is:

In determining the refractive index of a glass slab using a travelling microscope,the following readings are tabulated:
$(a)$ Reading of travelling microscope for ink mark $= 5.123 \ cm$
$(b)$ Reading of travelling microscope for ink mark through glass slab $= 6.123 \ cm$
$(c)$ Reading of travelling microscope for chalk dust on glass slab $= 8.123 \ cm$
From the data,the refractive index of a glass slab is:

$A$ light ray enters a rectangular glass slab of refractive index $\sqrt{3}$ at an angle of incidence of $60^{\circ}$. It travels a distance of $5 \, cm$ inside the slab and emerges out. What is the perpendicular distance between the incident and emergent ray?

In the given diagram,the apparent velocity of a bird (coming toward a fish) as seen by the fish is $19 \, cm/s$. Find the actual velocity of the bird in $cm/s$.