A Thin Prism: The Small-Angle Approximation

1 · Predict

A prism with a small apex angle (a 'thin prism') deviates light only gently. Does the deviation stay roughly constant across a range of incidence angles, unlike a wide-apex prism's more dramatic minimum-deviation curve?

• Yes — for a thin prism, deviation is approximately δ ≈ (n−1)A, staying nearly constant across a typical range of incidence angles near normal.
• Deviation still varies dramatically with incidence angle, just like a wide-apex prism.
• A thin prism produces essentially zero deviation.

2 · Set Up

1. Open the small-apex-prism preset and press Reset. This thin prism has apex angle A = 30°, index n = 1.5.
2. Enable the total-deviation readout.
3. Set the incidence angle for each trial and record the total deviation.

3 · Collect Data

Plot deviation δ (y-axis) against incidence angle θ₁ (x-axis) for your three trials. Is the curve much flatter than the white-light-prism experiment's?

4 · Analyze

1. For one trial, compute θ₂ = asin(sin θ₁/n), θ₃ = A − θ₂, θ₄ = asin(n·sin θ₃), then δ = θ₁ + θ₄ − A, using A = 30°, n = 1.5. Compare to the table. Also compute the thin-prism approximation δ ≈ (n−1)A = 15° and see how close your exact values land.
2. Explain why a smaller apex angle makes the total deviation less sensitive to the exact incidence angle — the thin-prism approximation δ ≈ (n−1)A drops the angle dependence entirely, valid when A is small.

5 · Extend

1. Thin prisms ('optical wedges') are used in some corrective glasses and rangefinders precisely because their near-constant deviation makes them predictable and easy to design with. Explain why a wide-apex prism's sharply angle-dependent deviation would be a poor choice for a simple corrective wedge.
2. Compare your deviation range here to the white-light-prism experiment's much wider swings. Explain why a bigger apex angle amplifies the angle-dependence of deviation, while a small apex angle nearly eliminates it.

The Physics Behind This Experiment

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