$A$ light ray is incident perpendicularly to one face of a $90^{\circ}$ prism and is totally internally reflected at the glass-air interface. If the angle of incidence at the interface is $45^{\circ}$,we conclude that the refractive index $n$ is:

Consider a glass prism immersed in a liquid as shown below. The refractive index of glass and liquid is $1.5$ and $1.2$, respectively. $A$ ray of light enters the prism perpendicular to the face $AB$. If the ray is totally internally reflected at the face $AC$, then the largest value of angle $\theta$ is:

$A$ ray of light incident normally on an isosceles right-angled prism travels as shown in the figure. The least value of the refractive index of the prism must be

If $\mu_1$ and $\mu_2$ are the refractive indices of the materials of core and cladding of an optical fibre,then the loss of light due to its leakage can be minimised by having

$A$ point source of light is placed at a depth $h = 0.5 \, m$ below the surface of a liquid $(\mu = \frac{5}{4})$. Then,the fraction of light energy that escapes directly from the liquid surface is:

$(a)$ Figure shows a cross-section of a 'light pipe' made of a glass fibre of refractive index $1.68$. The outer covering of the pipe is made of a material of refractive index $1.44$. What is the range of the angles of the incident rays with the axis of the pipe for which total internal reflections inside the pipe take place,as shown in the figure.
$(b)$ What is the answer if there is no outer covering of the pipe?