Question

Draw (i – δ) curve for a triangular prism and show the angle of minimum deviation.

Hint:

The plot of deviation versus incidence is a U-shaped curve; its single lowest point is \(\delta_m\), where \(i = e\).

Answer 1

Step 1: Understand the quantities.
Here \(i\) is the angle of incidence at the first face of a triangular prism and \(\delta\) is the angle of deviation of the emergent ray from the original direction.

Step 2: Describe the shape of the curve.
When \(\delta\) (Y-axis) is plotted against \(i\) (X-axis), the graph is a U-shaped (concave-up) curve. As \(i\) increases from a small value, the deviation \(\delta\) first decreases, reaches a single lowest point, and then increases again.

Step 3: Locate the minimum deviation.
The lowest point of this curve gives the angle of minimum deviation \(\delta_m\). At this point only one value of \(i\) produces the minimum; the ray passes symmetrically through the prism, so the angle of incidence equals the angle of emergence \((i = e)\) and the refracted ray inside the prism is parallel to the base.

Step 4: The diagram.
Draw the horizontal axis labelled \(i\) and the vertical axis labelled \(\delta\). Sketch a smooth U-shaped curve. Mark the bottom of the U with a horizontal dashed line meeting the \(\delta\)-axis at \(\delta_m\); this dashed level is the angle of minimum deviation.

\[\boxed{\text{The } i\text{-}\delta \text{ curve is U-shaped; its lowest point marks } \delta_m.}\]