$A$ tank is filled with water to a height of $16 \text{ cm}$. Find the apparent depth of a needle lying at the bottom of the tank as measured by a microscope. The refractive index of water $(\mu_{w})$ is $\frac{4}{3}$. (in $\text{ cm}$)

$A$ light ray is incident on a spherical glass surface at an angle $\alpha$ and is refracted at an angle $\beta$. What is the angle of deviation between the emergent ray and the incident ray?

$A$ tank is filled with water to a height of $12.5 \;cm$. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be $9.4 \;cm$. What is the refractive index of water?
If water is replaced by a liquid of refractive index $1.63$ up to the same height,by what distance would the microscope have to be moved to focus on the needle again?

According to the Cartesian sign convention in ray optics,

The absolute refractive indices of glass and water are $\frac{3}{2}$ and $\frac{4}{3}$,respectively. The ratio of the velocity of light in glass to that in water will be:

Assertion $(A)$: The colour of radiation does not change on passing through different media.
Reason $(R)$: The media do not absorb or emit colours.