Physics · JEE Advanced only

Deviation and Dispersion of Light by a Prism (JEE Advanced)

Not in the JEE Main syllabus, but it is in JEE Advanced. Study time: about 4-5 hours: 1.5 hours for theory and derivations, 1.5 hours for thin prism and dispersion concepts, 1-2 hours for prism combinations and problem practice.

Last updated: 26 October 2026

Direct answer

Deviation and dispersion of light by a prism deals with how light bends when passing through a prism and how white light splits into its component colors.

Deviation and dispersion of light by a prism deals with how light bends when passing through a prism and how white light splits into its component colors. Deviation refers to the angle by which light is bent from its original path, while dispersion refers to the separation of light into different wavelengths because each color refracts by a different amount.

Official syllabus

What the JEE Advanced syllabus says

“Deviation and dispersion of light by a prism”

Source: JEE Advanced 2026 Information Bulletin, Annexure-I. Closest JEE Main topic: refraction of light through a prism.

JEE Main covers basic refraction through a prism, but Advanced goes deeper into minimum deviation conditions, angular dispersion, dispersive power, and combinations of prisms for achromatic and direct vision arrangements. You need to master these quantitative relationships and prism combinations that Main does not test.

Key ideas

What you must understand

Deviation (δ) is the angle between incident ray and emergent ray; it depends on angle of incidence, prism angle, and refractive index
Minimum deviation occurs when the ray passes symmetrically through the prism (i = e, and the ray inside is parallel to the base)
Dispersion happens because refractive index varies with wavelength; violet bends most, red bends least
Angular dispersion is the difference in deviation between violet and red rays: θ = δ_v − δ_r
Dispersive power (ω) measures how much a material disperses light relative to its mean deviation: ω = (μ_v − μ_r)/(μ_y − 1)
Achromatic combination uses two prisms to produce deviation without dispersion; direct vision prism produces dispersion without net deviation

Formulas

Formulas and key facts

δ = (i + e) − A, where i = incidence angle, e = emergence angle, A = prism angle
At minimum deviation: i = e, r₁ = r₂ = A/2, and δ_min = 2i − A
μ = sin[(A + δ_min)/2] / sin(A/2)
For thin prism (small A): δ = (μ − 1)A
Angular dispersion: θ = (μ_v − μ_r)A for thin prism
Dispersive power: ω = (μ_v − μ_r)/(μ_y − 1)
Achromatic condition: ω₁A₁ + ω₂A₂ = 0 (opposite sign prisms)
Direct vision condition: (μ₁ − 1)A₁ = (μ₂ − 1)A₂

Avoid

Common mistakes

Confusing deviation with dispersion: deviation is total bending, dispersion is the spreading of colors
Forgetting that minimum deviation formula μ = sin[(A + δ_min)/2]/sin(A/2) only applies at minimum deviation condition
Using thin prism approximations (δ = (μ−1)A) for prisms with large angles where the approximation breaks down
In achromatic combinations, forgetting that the two prisms must have opposite orientations (one flint, one crown) and the condition involves dispersive powers, not just angles

Worked example

A JEE Advanced-level example

Question. A thin prism of angle 6° made of glass with μ_v = 1.56 and μ_r = 1.52 is combined with another thin prism of angle A₂ made of a different glass with μ_v = 1.72 and μ_r = 1.66. Find the angle A₂ of the second prism for the combination to be achromatic. Also find the net deviation for yellow light if μ_y = 1.54 for the first prism and μ_y = 1.69 for the second.

Show solution

For achromatic combination, total angular dispersion = 0: (μ_v1 − μ_r1)A₁ + (μ_v2 − μ_r2)A₂ = 0
Substituting values: (1.56 − 1.52)(6°) + (1.72 − 1.66)(A₂) = 0
This gives: (0.04)(6°) + (0.06)(A₂) = 0, so 0.24° + 0.06A₂ = 0
Solving: A₂ = −0.24°/0.06 = −4° (negative sign means opposite orientation)
Net deviation for yellow: δ_net = (μ_y1 − 1)A₁ + (μ_y2 − 1)A₂ = (0.54)(6°) + (0.69)(−4°)
δ_net = 3.24° − 2.76° = 0.48°

Answer: A₂ = 4° (opposite orientation to first prism), Net deviation = 0.48° in the direction of the first prism

Solved twice independently; both solutions agree.

FAQs

Frequently asked questions

Is Deviation and Dispersion of Light by a Prism in the JEE Main syllabus?

No. It is in the JEE Advanced 2026 syllabus only. The closest JEE Main topic is refraction of light through a prism.

How long does Deviation and Dispersion of Light by a Prism take to prepare for JEE Advanced?

About 4-5 hours: 1.5 hours for theory and derivations, 1.5 hours for thin prism and dispersion concepts, 1-2 hours for prism combinations and problem practice, if you already know the related JEE Main topic.