The figure shows a mixture of blue,green,and red colored rays incident normally on a right-angled prism. The critical angles of the material of the prism for red,green,and blue are $46^{\circ}$,$44^{\circ}$,and $43^{\circ}$ respectively. The arrangement will separate:

$(a)$ 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?

In the figure,$ABC$ is the cross-section of a right-angled prism and $BCDE$ is the cross-section of a glass slab. The value of $\theta$ so that light incident normally on the face $AB$ does not cross the face $BC$ is (given $\sin^{-1}(3/5) = 37^o$):

White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected,then the emerging ray in air contains:

For total internal reflection to take place,the angle of incidence $i$ and the refractive index $\mu$ of the medium must satisfy the inequality

$A$ light ray falls on a square glass slab as shown in the diagram. The index of refraction of the glass,if total internal reflection is to occur at the vertical face,is equal to