Relation between angles in a prism:
In optics, when light passes through a prism, it undergoes refraction which causes the light ray to bend. The bending of light depends on the angle of incidence, angle of emergence, angle of deviation, and angle of the prism.

Angle of Incidence (i):
The angle of incidence is the angle between the incident ray and the normal to the surface of the prism at the point of incidence.

Angle of Deviation (D):
The angle of deviation is the angle between the incident ray and the emergent ray when passing through the prism.

Angle of Emergence (e):
The angle of emergence is the angle between the emergent ray and the normal to the surface of the prism at the point of emergence.

Angle of Prism (A):
The angle of prism is the angle between the two refracting surfaces of the prism.

Relation between the angles:
The correct relation between the four angles is given by option B, which states that "A * D = i * e".

Explanation:
When light passes through a prism, it undergoes refraction twice, once at each surface of the prism. The angle of incidence and angle of emergence are measured with respect to the normal to the surface of the prism at the point of incidence and emergence respectively.

The angle of deviation is the angle between the incident ray and the emergent ray. This angle depends on both the angle of incidence and the angle of emergence.

The angle of prism is a fixed angle, determined by the geometry of the prism.

According to Snell's law of refraction, the ratio of the sine of the angle of incidence to the sine of the angle of emergence is constant for a given pair of media. This means that the product of the angle of incidence and angle of emergence is constant.

Mathematically, we can write it as:
sin(i)/sin(e) = constant

Now, let's consider the angles A, D, i, and e. The angle of deviation D depends on both the angle of incidence i and angle of emergence e. We can write it as:
D = i + e - A

Rearranging the equation, we get:
D = (i - A) + (e - A)

Now, substituting the value of (i - A) as x and (e - A) as y, we get:
D = x + y

This means that the angle of deviation D is the sum of the differences between the angle of incidence and the angle of prism, and the angle of emergence and the angle of prism.

Therefore, we can conclude that A * D = i * e, which is the correct relation between the angles.