$A$ mark at the bottom of a liquid appears to rise by $0.1 \ m$. The depth of the liquid is $1 \ m$. The refractive index of the liquid is

According to the Cartesian sign convention in ray optics,

An observer can see the top of a thin rod of height $h$ through a pinhole. The height of the container is $3h$ and its radius is $2h$. When the container is filled with a liquid up to a height of $2h$,the observer can see the bottom end of the rod. Find the refractive index of the liquid.

$A$ 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 $\text{ cm}$)

Light enters from air into a given medium at an angle of $45^{\circ}$ with the interface of the air-medium surface. After refraction,the light ray is deviated through an angle of $15^{\circ}$ from its original direction. The refractive index of the medium is

The length of the optical path of two media in contact of lengths $d_1$ and $d_2$ with refractive indices $\mu_1$ and $\mu_2$ respectively,is