The refractive index of a medium is $\mu$ and the wavelength of light in that medium is $\lambda$. Which of the following proportionality relations is correct?

Write two definitions and equations of relative refractive index.

$A$ glass slab consists of thin uniform layers of progressively decreasing refractive indices $(RI)$ such that the $RI$ of any layer is $\mu - m \Delta \mu$. Here, $\mu$ and $\Delta \mu$ denote the $RI$ of the $0^{\text{th}}$ layer and the difference in $RI$ between any two consecutive layers, respectively. The integer $m = 0, 1, 2, 3, \ldots$ denotes the number of the successive layers. $A$ ray of light from the $0^{\text{th}}$ layer enters the $1^{\text{st}}$ layer at an angle of incidence of $30^{\circ}$. After undergoing the $m^{\text{th}}$ refraction, the ray emerges parallel to the interface. If $\mu = 1.5$ and $\Delta \mu = 0.015$, the value of $m$ is:

Light of wavelength $300 \ nm$ in medium $A$ enters into medium $B$ through a plane surface. If the frequency of light is $5 \times 10^{14} \ Hz$ and the ratio of speed in medium $A$ to that in medium $B$ is $\frac{4}{5}$,the absolute refractive index of medium $B$ is:

An object is immersed in a fluid. In order that the object becomes invisible,it should

$A$ light ray of frequency '$v$' and wavelength '$\lambda$' enters a liquid of refractive index $\frac{3}{2}$. The ray travels in the liquid with: