Prism: Angle of Minimum Deviation
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flagWhat you'll discover
- arrow_forwardTrace a ray through a prism using Snell’s law at both faces
- arrow_forwardRecord (i, D) pairs and plot the deviation curve
- arrow_forwardLocate the minimum deviation Dₘ and the symmetry i = e
- arrow_forwardCompute n = sin((A + Dₘ)/2) / sin(A/2)
Geometry of deviation
Light entering a prism refracts toward the normal at the first face, crosses the glass, and refracts away at the second face. Two relations carry the whole experiment: r₁ + r₂ = A (the refraction angles meet the apex angle) and D = i + e − A (total deviation is what is left of the entry and exit bends).
As you raise i from grazing values, D first decreases, reaches a single minimum Dₘ, then increases — a U-shaped curve. At the minimum the ray passes SYMMETRICALLY: i = e, r₁ = r₂ = A/2, and the ray inside runs parallel to the base. Symmetry is why the minimum is unique.
From Dₘ to the refractive index
At minimum deviation, Snell’s law at the first face reads sin i = n sin r₁ with i = (A + Dₘ)/2 and r₁ = A/2. Hence n = sin[(A + Dₘ)/2] / sin(A/2). For a 60° crown-glass prism, Dₘ ≈ 39° gives n ≈ 1.52.
In the pin-and-paper version of this practical you fix the prism on drawing paper, prick two pins along an incident ray and two along the emergent ray, then measure i and D with a protractor for many incidence angles. The simulation replaces the pins with a draggable ray but the data analysis — table, curve, minimum — is identical.
Reading the minimum well, and TIR surprises
The curve is FLAT near its minimum, which is both a gift and a trap: a small error in i barely changes D (gift), but eyeballing the exact minimum from a couple of points is unreliable (trap). Take many points spaced a few degrees apart around the dip and read Dₘ from a smooth curve through them, never from a single measurement.
At small incidence angles you may find no emergent ray at all: r₂ exceeds the critical angle and the ray suffers total internal reflection inside the prism. Note it, then continue at larger i. Other precautions: pins (or rays) well separated for direction accuracy, sharp pencil prism outline, protractor read to half a degree, and the same prism face used as entry face throughout.