Which of the following graphs shows the appropriate variation of refractive index $\mu$ with wavelength $\lambda$?

An opaque sphere of radius $a$ is just immersed in a transparent liquid as shown in the figure. $A$ point source is placed on the vertical diameter of the sphere at a distance $a/2$ from the top of the sphere. One ray originating from the point source after refraction from the air-liquid interface forms a tangent to the sphere. The angle of refraction for that particular ray is $30^{\circ}$. The refractive index of the liquid is:

$A$ ray of light is incident on a transparent sphere at an angle of $\pi / 4$ and is refracted at an angle $r$. The ray emerges from the sphere after suffering one internal reflection. The total angle of deviation of the ray is

As shown in the figure,after passing through medium $1$,the speed of light $v_{2}$ in medium $2$ will be $..... \times 10^{8} \, ms^{-1}$. (Given $c = 3 \times 10^{8} \, ms^{-1}$)

If the wavelength of light in air is $4200\, \mathring A$,what will be the wavelength of light in water $(\mu = 4/3)$ in $\mathring A$?

An insect starts moving up in a liquid from point $O$ with a variable refractive index $\mu = \mu_0(1 + ay)$,where $y$ is the depth of the liquid from the surface. If $u$ is the speed of the insect,what is its apparent speed to the observer $E$?