What happens to the refractive index on heating the liquid?

The correct option is Decreases.

To understand why the refractive index of a liquid decreases upon heating, let us examine the relationship between temperature, density, and the refractive index of a substance.

The refractive index ($n$) of a medium is directly related to its density ($\rho$). According to the Gladstone-Dale relation (or the more rigorous Lorentz-Lorenz equation), the refractive index of a substance is given by:
$\frac{n^2-1}{n^2+2}·\frac{1}{\rho }=\text{constant}$
This indicates that the refractive index is directly proportional to the density of the medium.

When a liquid is heated, its temperature increases. This increase in temperature causes the molecules in the liquid to gain thermal energy and move more rapidly, increasing the average distance between them. As a result, the liquid expands in volume.

Since density is mass per unit volume ($\rho =m/V$), and the mass remains constant while the volume increases, the density of the liquid decreases upon heating.

With the decrease in density, the concentration of atoms or molecules per unit volume decreases, meaning there are fewer particles to interact with and slow down the light waves passing through. Consequently, the speed of light in the liquid increases, which corresponds to a lower refractive index. Therefore, heating a liquid leads to a decrease in its refractive index.