EXERCISE 13

The refractive of the material of a prism of refracting angle $45°$ is 1.6 for a certain monochromatic ray. What should be the minimum angle of incidence of this ray on the prism so that no total internal reflection takes place as the ray comes out of the prism? 

A parallel beam of light falls normally on the first face of a prism of small angle.The portion of the beam which is refracted at the second surface is deviated through an angle of $6°{30}^{\text{'}}$and the portion which is reflected at the second surface and emerges again at the first surface makes an angle of $1°{15}^{\text{'}}$With the direction of the incident beam. Calculate the angle of the prism and the refractive index of glass.

A ray of light within a glass slab immersed in water has critical angle $30°.$ If the slab is immersed in another medium of r.i. $\sqrt{2}$, what will be the critical angle?

A ray of light is incident at an angle of $60°$ on one face of prism which has an angle of $30°.$ The ray emerging out of the prism makes an angle of$30°$ with the incident ray show that the emergent ray is perpendicular to the face through which it emerges and calculate the refractive
index of the material of the lens.

Light is incident at an angle $\alpha$ on one planer end of a transparent cylindrical rod of refractive index n. Determine the least value of $n$ so that the light entering the rod does not emerge from the curved surface of rod irrespective of the value of $\alpha$. 

A B and C D are surfaces of two slabs Fig. $13.75$. The medium between the slabs has refractive index 2. R.I. of the slabs are $\sqrt{2}$ and $\sqrt{3}$ respectively. Find the minimum angle of incidence at Q, so that the ray is totally reflected by both slabs.

Light enters a prism of angle A at a grazing incidence to emerge at angle $\theta$ with the normal. Show that the refractive index of the material of the prism is given by

$\mu ={\left[1+{\left(\frac{\cos A+\sin \theta }{\sin A}\right)}^2\right]}^{\frac{1}{2}}$

A right-angled prism is kept immersed in water. When a ray of light is allowed to be incident on one of the faces of the prism adjoining the right angle normal to the face, the ray is found to be totally reflected by the face opposite to the right angle and to emerge through the other face adjoining the right angle. But when the ray of light is allowed to be normally incident on the other face adjoining the right angle, it emerges through the face opposite to the right angle and there is total internal reflection.

If the other two angles of the prism be $60°$ and $30°$, what information can you gather about the refractive index of the material of the prism? Given RI of water with respect to vacuum$=1.33$ and $V_3=1.732.$