Which of the following statements is correct?

Light of wavelength $\lambda$ in air enters a medium of refractive index $\mu$. Two points in this medium,lying along the path of this light,are at a distance $x$ apart. The phase difference between these points is:

$A$ vessel of height $2d$ is half-filled with a liquid of refractive index $\sqrt{2}$ and the other half with a liquid of refractive index $n$ (the given liquids are immiscible). Then the apparent depth of the inner surface of the bottom of the vessel (neglecting the thickness of the bottom of the vessel) will be

The optical path of a monochromatic light is the same if it goes through $4.0 \, cm$ of glass or $4.5 \, cm$ of water. If the refractive index of glass is $1.53$,the refractive index of water is:

$AB$ is a boundary separating two media of different refractive indices. $A$ ray is incident on the boundary and is partially reflected and partially transmitted. Choose the $\text{CORRECT}$ statement.

$A$ light ray incident along a vector $\vec{AO}$ $(\vec{AO} = 2\hat{i} - 3\hat{j})$ emerges along a vector $\vec{OB}$ $(\vec{OB} = C\hat{i} - 4\hat{j})$ as shown in the figure. The value of $C$ is . . . . . . .