$A$ beam of light is propagating at an angle $\alpha_1$ from medium $1$ into medium $2$ at an angle $\alpha_2$. If the wavelength of light in medium $1$ is $\lambda_1$, then the wavelength of light in medium $2$, $\lambda_2$, is:

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$: Refractive index of glass is higher than that of air.
Reason $(R)$: Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.
In the light of the above statements,choose the most appropriate answer from the options given below.

Monochromatic light of wavelength $589 \; nm$ is incident from air on a water surface. What are the wavelength,frequency,and speed of
$(a)$ reflected,and
$(b)$ refracted light? Refractive index of water is $1.33$.

$A$ pole is vertically submerged in a swimming pool such that it casts a shadow of length $2.15 \, m$ within the water when sunlight is incident at an angle of $30^{\circ}$ with the water surface. If the swimming pool is filled to a height of $1.5 \, m$,then the height of the pole above the water surface in centimeters is $(\mu_W = 4/3) .........$

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 $E$?

Give one example of a substance whose mass density is low but optical density is high.