Prism and Ray Optics for JEE Main: Complete Guide

Ray optics and prisms contribute three to five questions every JEE Main session, making this one of the most reliably tested optics topics. The key formulas are compact and the problem patterns repeat closely across years. Prism-related questions particularly reward students who know the minimum deviation condition and the refractive index formula — this alone can secure four to six marks in seconds.

Snell's Law and Total Internal Reflection

Snell's law: n₁ sinθ₁ = n₂ sinθ₂. At the critical angle θ_c, the refracted ray lies along the interface: sinθ_c = n₂/n₁ (for n₁ > n₂). Beyond θ_c, total internal reflection occurs — the ray reflects entirely back into the denser medium. Applications: optical fibres, diamonds (high n, small θ_c), and mirages. A diamond has n ≈ 2.42, giving θ_c ≈ 24.4° — extremely small, maximising brilliance through multiple total reflections. For the broader optics context see our ray and wave optics guide.

Prism: Deviation and Refraction Equations

For a prism of apex angle A, the ray refracts at both surfaces. If r₁ and r₂ are angles of refraction at the two faces: r₁ + r₂ = A. The angle of deviation δ = (i₁ + i₂) − A, where i₁ and i₂ are angles of incidence. Snell's law applies at each surface: n sin r₁ = sin i₁ and n sin r₂ = sin i₂. Memorise these four equations; every prism numerical combines them.

Minimum Deviation and the n Formula

At minimum deviation δ_m, the ray passes symmetrically (r₁ = r₂ = A/2; i₁ = i₂). The refractive index formula is: n = sin[(A + δ_m)/2] / sin(A/2). This is the single most important prism formula. If A = 60° and δ_m = 30°: n = sin(45°)/sin(30°) = (1/√2)/(1/2) = √2. This template — substitute, simplify, calculate — works for every minimum-deviation numerical. In JEE, if a prism problem gives both A and δ_m, apply this formula immediately.

Dispersion and Dispersive Power

Different colours refract by different amounts because n varies with wavelength (dispersion). Violet deviates most (highest n), red least. The angular dispersion Δδ = δ_violet − δ_red ≈ (n_v − n_r) × A for small angles. Dispersive power ω = (n_v − n_r)/(n − 1) where n is the mean refractive index. An achromatic combination of two prisms satisfies ω₁A₁ = ω₂A₂ — this equal-and-opposite dispersive power condition eliminates net dispersion. JEE tests this condition directly in problems on combining prisms.

Lenses and the Lensmaker's Formula

The lensmaker's formula: 1/f = (n − 1)(1/R₁ − 1/R₂). The thin-lens formula: 1/v − 1/u = 1/f (using Cartesian sign convention). Magnification m = v/u. For lenses in contact: 1/f_net = 1/f₁ + 1/f₂ (power adds). Power P = 1/f in dioptres (f in metres). After mastering these along with prism formulas, test yourself with a free mock test that covers the full optics section, then target weak spots in our optics numericals guide.