(a) (i) Refraction through a Triangular Prism
Step 1 (Diagram and Governing Laws): [1.5 Marks]
The path of a light ray through a prism is governed by Snell's Law at each interface. The ray $PQ$ enters the prism at angle $i$, refracts at $r_1$, hits the second face at $r_2$, and emerges at angle $e$.
[Note: Student must draw a neat ray diagram showing the prism, incident ray, refracted ray, emergent ray, angle of deviation ($\delta$), and angle of prism ($A$).]
Governing relations:
- In quadrilateral $AQNR$: $\angle A + \angle QNR = 180^\circ$
- In $\triangle QNR$: $r_1 + r_2 + \angle QNR = 180^\circ$
Step 2 (Step-by-Step Mathematical Working): [2.5 Marks]
From the geometry of the prism:
$$A = r_1 + r_2 \quad \dots(1)$$The total deviation $\delta$ produced by the prism is the sum of deviations at the two faces:
$$\delta = (i - r_1) + (e - r_2)$$ $$\delta = (i + e) - (r_1 + r_2)$$Substituting equation (1) into the expression for $\delta$:
$$\delta = i + e - A$$This is the required expression for the angle of deviation.
Step 3 (Graph and Final Conclusion): [1.0 Mark]
The graph of $\delta$ versus $i$ is a parabolic curve. It shows that for a given prism, there is a unique angle of incidence for which the deviation is minimum ($\delta_m$).
[Note: The graph must show $\delta$ on the y-axis and $i$ on the x-axis, with the curve starting from a point, dipping to a minimum, and rising again.]
Final Result: The relationship is given by $\delta = i + e - A$.
💡 EL10 Concept Insight: Imagine light walking through a prism like a person walking through a crowded room; the prism forces the light to bend twice, and the total "turn" it makes is simply the sum of the two bends minus the fixed angle of the prism's corner.