Animated Solution for Physics - Optics: The expected graphical representation of the variation of angle of deviation $\delta$ with angle of incidence $i$ in a prism is

Imagine a ray of light traveling through the air and striking the smooth, angled surface of a glass prism. As it enters, it bends. As it exits the other side, it bends again. This total change in direction, the angle between the original path and the final path, is what we call the angle of deviation, denoted by $\delta$.

But here is the fascinating part: this deviation isn't constant. It is highly sensitive to the angle at which the light initially strikes the prism, known as the angle of incidence, $i$. The relationship between these two angles tells a beautiful story of symmetry and optics.

When we start with a very small angle of incidence, the light ray is forced to bend sharply, resulting in a large angle of deviation. As we gradually increase the angle of incidence, the angle of deviation begins to drop. If we were to plot this on a graph, the curve would start high and slope downwards.

However, it doesn't keep dropping forever.

At one specific, magical angle of incidence, something special happens. The light ray travels through the prism perfectly parallel to its base. The angle at which it enters the prism exactly equals the angle at which it emerges ($i=e$).

Because of this perfect geometric symmetry, the light ray undergoes the least possible bending. This lowest point on our graph is called the angle of minimum deviation, ${\delta }_m$.

What happens if we keep increasing the angle of incidence beyond this point of symmetry? The symmetry is broken, and the angle of deviation starts to climb back up.

This creates a distinct U-shaped curve. A beautiful consequence of this shape is the principle of reversibility. If you draw a horizontal line across the graph for any deviation greater than the minimum, it will intersect the curve at two distinct points. This means that for any given deviation, there are exactly two possible angles of incidence ($i_1$ and $i_2$). If a ray enters at $i_1$, it exits at $i_2$. If it enters at $i_2$, it exits at $i_1$.

Therefore, the correct graphical representation of the variation of the angle of deviation with the angle of incidence is the U-shaped curve, which corresponds to option (b).