Question:easy

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

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The plot of deviation versus incidence is a U-shaped curve; its single lowest point is \(\delta_m\), where \(i = e\).
Updated On: Jul 10, 2026
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Solution and Explanation

Step 1: Set up the axes.
Take the angle of incidence \(i\) along the horizontal axis and the angle of deviation \(\delta\) along the vertical axis for light passing through a triangular (60°) prism.

Step 2: Trace how deviation changes.
For a very small \(i\) the emergent ray bends a lot, so \(\delta\) is large. As \(i\) grows, \(\delta\) falls, hits a single minimum, and then rises again for larger \(i\). This produces a curve that dips in the middle, like a valley.

Step 3: Meaning of the valley bottom.
The lowest point of the valley is the angle of minimum deviation \(\delta_m\). A key feature is that a given \(\delta\) (except \(\delta_m\)) can be produced by two different angles of incidence, but \(\delta_m\) corresponds to exactly one angle of incidence, where \(i = e\) and the ray inside runs parallel to the base.

Step 4: Marking on the sketch.
On the U-shaped curve, drop a horizontal dashed line from the turning point to the \(\delta\)-axis and label that value \(\delta_m\); drop a vertical dashed line to the \(i\)-axis to show the corresponding incidence angle.

\[\boxed{\delta_m \text{ = ordinate of the lowest point of the } i\text{-}\delta \text{ graph}}\]
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