What should be the maximum acceptance angle at the air-core interface of an optical fibre if $n_1$ and $n_2$ are the refractive indices of the core and the cladding,respectively?

On the hypotenuse of a right-angled prism $(30^{\circ}-60^{\circ}-90^{\circ})$ with a refractive index of $1.50$,a drop of liquid is placed as shown in the figure. Light is allowed to fall normally on the short face of the prism. In order for the ray of light to undergo total internal reflection at the hypotenuse,what is the maximum value of the refractive index of the liquid?

$A$ point source of light is placed $4 \; m$ below the surface of water of refractive index $5/3$. The minimum diameter of a disc which should be placed over the source on the surface of water to cut-off all light coming out of water is ... $m$.

$A$ glass prism of refractive index $1.5$ is immersed in water (refractive index $4/3$). $A$ light beam incident normally on the face $AB$ is totally reflected to reach the face $BC$ if

Three rays of light,namely red $(R)$,green $(G)$ and blue $(B)$ are incident on the face $PQ$ of a right-angled prism $PQR$ as shown in the figure. The refractive indices of the material of the prism for red,green and blue wavelengths are $1.27$,$1.42$ and $1.49$ respectively. The colour of the ray$(s)$ emerging out of the face $PR$ 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?