Minimum Deviation: Symmetric Passage Through a Prism

1 · Predict

A ray through a prism achieves its smallest possible deviation angle at one special incidence angle — symmetric passage, where the ray inside the prism travels parallel to its base. Does a wider-apex prism have a larger minimum deviation?

• Yes — a bigger apex angle bends the ray more overall, giving a larger minimum deviation.
• A bigger apex angle gives a smaller minimum deviation.
• Minimum deviation doesn't depend on the apex angle.

2 · Set Up

1. Open the min-deviation preset and press Reset. This 60°/n=1.5 prism is set to its symmetric-passage incidence angle, which minimizes deviation.
2. Enable the deviation readout.
3. Set the apex angle for each trial (index n = 1.5 fixed) and record the minimum deviation.

3 · Collect Data

Plot δ_min (y-axis) against apex angle A (x-axis) for your three trials. Is the line straight?

4 · Analyze

1. For one trial, compute δ_min = 2·asin(n·sin(A/2)) − A using n = 1.5. Compare to the table.
2. Explain why symmetric passage (the ray traveling parallel to the prism's base inside the glass) gives the smallest possible deviation for a given apex angle and index — any other incidence angle produces MORE deviation, not less.

5 · Extend

1. The minimum-deviation formula can be inverted to MEASURE a glass's refractive index from an apex angle and a measured minimum deviation: n = sin((A+δ_min)/2)/sin(A/2). This is the classic prism-spectrometer technique. Why might finding the minimum experimentally (by slowly rotating the prism and watching for where deviation stops decreasing) be more reliable than measuring at an arbitrary incidence angle?
2. A larger apex angle prism spreads white light into a wider spectrum. Explain, using your δ_min-vs-A relationship, why spectrometer designers might choose a larger apex angle when they need finer wavelength resolution.

The Physics Behind This Experiment

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