The expected graphical representation of the variation of angle of deviation '$$\delta$$' with angle of incidence 'i' in a prism is:

We need to determine the expected graphical representation showing how the angle of deviation ($$\delta$$) varies with the angle of incidence ($$i$$) for a light ray passing through a prism.

1. Understand the Relationship Between $$\delta$$ and $$i$$

From experimental observations in optics, as the angle of incidence ($$i$$) increases starting from a small initial value:

• The angle of deviation ($$\delta$$) first decreases until it reaches a specific localized minimum value.
• This lowest point on the curve is known as the angle of minimum deviation ($$\delta_m$$). At this specific point, the angle of incidence equals the angle of emergence ($$i = e$$).
• If the angle of incidence is increased further beyond this minimum point, the angle of deviation reverses direction and begins to increase continuously.

2. Analyze the Shape of the Curve

The relationship results in an asymmetric, continuous, U-shaped (parabolic-like) curve that opens upward on a coordinate system where the vertical axis represents $$\delta$$ and the horizontal axis represents $$i$$.

Reviewing the options visible on the page:

• Option A: Shows an inverted U-shape (an initial increase followed by a decrease), which is incorrect.
• Option B (marked with the green checkmark): Correctly displays a smooth curve starting high, sloping downwards to a minimum point, and then curving upwards as the angle of incidence increases.

Conclusion

The correct graphical representation of the variation of the angle of deviation with the angle of incidence in a prism is given by Option B.