K K Sharma Solutions for Chapter: Ray Optics and Optical Instruments, Exercise 1: TOPICWISE QUESTIONS

A ray of light is incident at an angle $i$ from denser to the rarer medium: The reflected and the refracted rays are mutually perpendicular. If the angle of reflection and the angle of refraction are $r$ and $r\text{'}$ respectively, then the critical angle will be 

A ray of light is incident at an angle of ${45}^{\circ }$ from air to a glass slab at point $A,$ the angle of incidence being ${45}^{\circ }$. The minimum value of the refractive index of the material of the slab so that TIR takes place at $B$ is

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 $\left(\text{Given}: {\sin }^{-1}\left(\frac{3}{5}\right) = 37°\right)$

A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}$. It is surrounded by air. A light ray is incident at the midpoint of one end of the rod as shown in the figure.

The incident angle ($\theta$) for which the light ray grazes along the wall of the rod is

In the figure below, what should be the angle of incidence at $A$ of the spherical glass placed in air so that total internal reflection takes place at $B$?
  

A ray of light starts from midpoint $D$ of side $BC$ of an equilateral triangular prism $ABC$ kept in air and moves along $EA$, where $E$ is the midpoint of side $AC$. The refractive index of prism is 

A ray of light makes a normal incidence on the diagonal face of a right-angled prism as shown in the figure such that the ray strikes the surface AB of the prism after entering the prism. If $\theta = {37}^{\circ }$, then the angle of deviation is $\left(\sin {37}^{\circ } =\frac{3}{5}\right)$

A ray of light enters into the prism normally through face $1$ and comes out normally through face $3$. The minimum refractive index of the prism is