$A$ right-angled glass prism is shown in the figure. $A$ liquid film is in contact with the hypotenuse face. $A$ ray of light incident normally on the face $AB$ will undergo total internal reflection from the hypotenuse face,if the refractive index of the liquid is $\mu_l$ (given $\mu_{\text{glass}} = 3/2$).

$A$ transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. $A$ light ray is incident at the mid-point of one end of the rod as shown in the figure. The incident angle $\theta$ for which the light ray grazes along the wall of the rod is

In an optical fibre, the core and cladding are made with materials of refractive indices $1.5$ and $1.414$ respectively. To observe total internal reflection, what will be the range of the incident angle with the axis of the optical fibre?

The speed of light in media $M_1$ and $M_2$ are $1.5 \times 10^8 \ m/s$ and $2.0 \times 10^8 \ m/s$ respectively. $A$ ray of light enters from medium $M_1$ to $M_2$ at an incidence angle $i$. If the ray suffers total internal reflection,the value of $i$ is

$A$ point source $S$ is placed at the bottom of different layers as shown in the figure. The refractive index of the bottom-most layer is $\mu_0$. The refractive index of any other upper layer is $\mu(n) = \mu_0 - \frac{\mu_0}{4n - 18}$,where $n = 1, 2, \dots$. $A$ ray of light with an angle of incidence $i$ slightly more than $30^\circ$ starts from the source $S$. Total internal reflection takes place at the upper surface of a layer having $n$ equal to

$A$ spider and a fly are on opposite sides of the surface of a glass sphere. What is the maximum solid angle $\Omega$ within which the fly can be seen by the spider?
Given: The dimensions of the spider and the fly are very small with respect to the sphere. The refractive index of the glass is $\mu_g = \sqrt{2}$.