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

$A$ ray of light travels from a medium of refractive index $\mu$ to air. Its angle of incidence in the medium is $i$,measured from the normal to the boundary,and its angle of deviation is $\delta$. If $\delta$ is plotted against $i$,which of the following best represents the resulting curve?

$A$ light wave travelling linearly in a medium of dielectric constant $4$ is incident on the horizontal interface separating the medium from air. The angle of incidence for which the total intensity of the incident wave will be reflected back into the same medium is (Given: relative permeability of the medium $\mu_{r} = 1$) (in $^{\circ}$)

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:

$A$ ray of light refracts from medium $1$ into a thin layer of medium $2$, crosses the layer, and is incident at the critical angle on the interface between medium $2$ and $3$ as shown in the figure. If the angle of incidence of the ray is $\theta$, the value of $\theta$ 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?