A

To analyze the scenarios provided in the columns, we need to understand the behavior of light when it interacts with different optical devices.
(i) A ray of white light is incident on one face of an equilateral prism:
When white light enters an equilateral prism, it undergoes refraction and subsequently dispersion due to the varying refractive indices of different wavelengths of light. This results in the light spreading out into its constituent colors, creating a divergent beam. Therefore, the result is [A] Divergent beam.
(ii) A ray of white light is incident at an angle on a thick glass sheet:
The behavior of the light will depend on the angle of incidence and the refractive index of the glass. If the angle is greater than the critical angle of the glass, total internal reflection may occur, leading to result [B] Total internal reflection. However, without specific details about the angle, we can't ascertain this result in general.
(iii) A ray of white light passes from optically denser medium to rarer medium:
This situation would lead to refraction, and the ray would bend away from the normal. There may also be a lateral shift, but the description does not match the stated result of lateral shift [C].
(iv) A parallel beam of monochromatic light passes symmetrically through a glass lens:
In this case, the light will be bent towards the focal point of the lens, so the statement about dispersion [D] does not match since the light is monochromatic and does not disperse into colors.
Therefore, the correct answer for (i) is [A] Divergent beam.