Optics
Thin (small-apex) prism
A thin prism (small apex) deviates light only slightly — the thin-prism limit δ ≈ (n−1)·A.
Thin (small-apex) prism — interactive Optics simulation. A thin prism (small apex) deviates light only slightly — the thin-prism limit δ ≈ (n−1)·A. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Thin prism
A thin prism (small apex) deviates light only slightly — the thin-prism limit δ ≈ (n−1)·A.
For a very small apex angle A, deviation approaches δ ≈ (n − 1)A—the thin-prism approximation used in eyeglass wedge prescriptions and fine adjustments. Large deviations require thicker prisms or higher index.
- δ ≈ (n−1)A
- Small apex angle
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
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?
Predictions to weigh
- Deviation still varies dramatically with incidence angle, just like a wide-apex prism.
- Yes — for a thin prism, deviation is approximately δ ≈ (n−1)A, staying nearly constant across a typical range of incidence angles near normal.
- A thin prism produces essentially zero deviation.
Variable roles
What you set:
- Incidence angle θ₁ (°)
What you measure:
- Total deviation δ (°)
How the investigation runs
- Open the small-apex-prism preset and press Reset. This thin prism has apex angle A = 30°, index n = 1.5.
- Enable the total-deviation readout.
- Set the incidence angle for each trial and record the total deviation.
Governing equation
Thin-Prism Approximation — δ = θ₁ + θ₄ − A
For a prism with a small apex angle A, the exact deviation formula simplifies to δ ≈ (n−1)A, nearly independent of incidence angle — the small-angle limit of the full Snell-law prism calculation.
What the printable worksheet asks students to work out
- 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.
- 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.
Where this shows up beyond the lab
- 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.
- 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.
- AP Physics 2 — Unit 13: Geometric Optics
- General High School Physics — Light & optics
- NGSS High School Physics — Wave properties
- Welcome to Small Apex Prism
- Select the prism
- Press Play
- Small deflection angle
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.