A ray of light travelling in air is incident at angle of incidence, i$\approx {90}^o$ on a long rectangular slab of a transparent medium of thickness $y_0$. The medium has a variable refraction index of $\mu \left(x\right)=\sqrt{1+e^{{}^{2x}/{}_a}}\forall x\ge 0$, where a is a positive constant. If $y_0=\frac{a}{2}$, then $x$ coordinates of the point where the ray intersects the upper surface of the slab-air boundary is a $ln$ $\left(N\right)$. Find the value of $N$ . ​​​​​​​

Q. A ray of light travelling in air is incident at grazing angle (incident angle $={90}^o$) on a long rectangular slab of a transparent medium of thickness $t=1.0m$. The point of incidence is the origin A(0, 0). The medium has a variable index of refraction n(y) given by
$n\left(y\right)=[k{y}^{3/2}+1{]}^{1/2}$
where $k=1.0(m{)}^{-3/2}$
a. Obtain a relation between the slope of the trajectory of ray at point B(x, y) in the medium and the incident angle at the point.
b. Obtain an equation for the trajectory y(x) of the ray in the medium.
c. Determine the coordinates $(x_1,y_1)$ of point P, where the ray intersects the upper surface of the slab-air boundary.
d. Indicate the path of the ray subsequently

Q. A ray of light travelling in a transparent medium falls on a surface separating the medium from air, at an angle of incidence of ${45}^{\circ }$. The ray undergoes total internal reflection. If $n$ is the refractive index of the medium with respect to air, select the possible values of $n$ from the following.

Q. A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence 45${}^{\circ }$. The ray undergoes total internal reflection. The possible value of refractive index of the medium with respect to air is

Q. A ray of light travelling in a medium of refractive index 2, is incident onto the flat surface of a slab, the angle of incidence is ${37}^o$. The refractive index of the material of the slab varies with depth ($x$) from the top surface, $\mu \left(X\right)=a-bx$, where $a=2,b=1m^{-1}$ and $x$ is in $m$. The maximum depth reached by the way is:

Q. A ray of light travelling in a transparent medium falls on a surface separating the medium from air at an angle of incidence ${40}^o$. The ray undergoes total internal reflection. If $n$ is the refractive index of the medium with respect to air, select the possible values of $n$ from the following$(Givensin{40}^o=0.64)$