If $_i{\mu _j}$ represents the refractive index when a light ray goes from medium $i$ to medium $j,$ then the product $_2{\mu _1} \times {\,_3}{\mu _2} \times {\,_4}{\mu _3}$ is equal to

There is a small air bubble at the centre of a solid glass sphere of radius $r$ and refractive index $\mu$. What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside?

The wavelength of light, while it is passing through water, is $540 \ nm$. The refractive index of water is $\frac{4}{3}$. The wavelength of the same light when it is passing through a transparent medium having a refractive index of $\frac{3}{2}$ is . . . . . . $nm$.

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

$A$ ray of light travelling through glass of refractive index $\sqrt{2}$ is incident on a glass-air boundary at an angle of incidence of $45^{\circ}$. If the refractive index of air is $1$,then the angle of refraction will be: $[\sin 45^{\circ} = \frac{1}{\sqrt{2}}, \sin 90^{\circ} = 1]$ (in $^{\circ}$)

$A$ 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 . . . . . . .