Monochromatic light of frequency $5 \times 10^{14} \ Hz$ travelling in vacuum enters a medium of refractive index $1.5$. Its wavelength in the medium is ....... $\mathring{A}$.

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

What are optically denser and optically rarer media?

$A$ 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 refractive index of water with respect to air is $4/3$ and the refractive index of glass with respect to air is $3/2$. The refractive index of water with respect to glass is

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 $E$?