Given below are two statements related to Young's double slit...

The angular width of interference fringes in Young's double slit experiment is given by $\theta = \dfrac{\lambda}{d}$, where $\lambda$ is the wavelength of light and $d$ is the separation between the slits.

If the separation between the slits is doubled ($d' = 2d$), the new angular width becomes $\theta' = \dfrac{\lambda}{2d} = \dfrac{\theta}{2}$. The angular width becomes half of its initial value. Thus, Statement I is false.

The linear fringe width is given by $\beta = \dfrac{\lambda D}{d}$. When the entire apparatus is immersed in a transparent liquid of refractive index $\mu > 1$, the wavelength of light in the liquid decreases to $\lambda' = \dfrac{\lambda}{\mu}$.

The new linear fringe width becomes $\beta' = \dfrac{\lambda' D}{d} = \dfrac{\beta}{\mu}$. Since $\mu > 1$, the linear fringe width decreases. Thus, Statement II is true.

Therefore, Statement I is false but Statement II is true.

Answer: Statement I is false but Statement II is true.