Refraction through a prism

What is refraction through a prism?

In plain words: a glass prism in air refracts light at two nonparallel faces, giving a net turn towards its thicker base in the usual transmitted-ray arrangement. Turn the prism slowly and the turning first gets smaller, then larger again. The smallest turning is special: the ray then passes through the prism symmetrically, and that angle tells you the refractive index of the glass.

Scope: a transparent isotropic prism of index higher than its surroundings, with the same surrounding medium on both faces, one colour of light, and rays in a plane perpendicular to the prism’s edge. The usual minimum-deviation formulas describe rays transmitted through the chosen pair of faces; total internal reflection limits which incidence angles are possible.

Angle of deviation

• In NCERT Figure 9.21 a ray PQ meets face AB at an angle of incidence i and refracts at r₁; inside, it meets face AC at r₂ and leaves at the angle of emergence e. The angle between the emergent ray RS and the incident ray PQ is the angle of deviation δ (NCERT page 239). Each refraction follows Snell’s law.
• In the quadrilateral AQNR (N is where the normals at Q and R meet), the angles at Q and R are right angles, so ∠A + ∠QNR = 180°. In triangle QNR, r₁ + r₂ + ∠QNR = 180°. Comparing the two (NCERT Eq. (9.34), page 239):

• The total deviation is the sum of the deviations at the two faces, δ = (i − r₁) + (e − r₂), so (NCERT Eq. (9.35), page 239):

Angle of minimum deviation

• A plot of δ against i is a curve with a minimum (NCERT page 239; Figure 9.22, page 240). Apart from the minimum, where i = e, each deviation in the allowed transmitted range (away from grazing endpoints) is reached for two values of i, and so of e. This follows from the symmetry of i and e in NCERT Eq. (9.35): the path of the ray can be traced backwards, giving the same deviation with i and e swapped (NCERT pages 239–240).
• At the minimum deviation D_m, the path is symmetric, i = e and r₁ = r₂ (NCERT page 240). So the ray inside makes equal angles with the two refracting faces. It runs parallel to the base only when the two faces are equally inclined to the base (AB = AC, as in an equilateral prism); NCERT’s statement that the ray becomes parallel to the base assumes such a prism (reasoned).
• So NCERT Eq. (9.34) gives 2r = A (NCERT Eq. (9.36)) and NCERT Eq. (9.35) gives D_m = 2i − A (NCERT Eq. (9.37), page 240):

Refractive index from the minimum deviation

• Putting these into Snell’s law at the first face, n₂₁ = sin i/sin r (NCERT Eq. (9.38), page 240):

• A and D_m can both be measured, so this gives a way to find the refractive index of the material of the prism (NCERT page 240).
• D_m depends on the medium around the prism through n₂₁: the same prism deviates light much less in water than in air (NCERT Exercise 9.6, page 249).

Thin prism

• For a prism of small angle A, D_m is also small, and the sines can be replaced by the angles in radians: n₂₁ ≈ [(A + D_m)/2]/(A/2), which gives (NCERT page 240):

• So thin prisms do not deviate light much (NCERT page 240). A 6° prism of crown glass (n = 1.52) deviates light by only about 3.1°.

Solved examples

Common mistakes to avoid

Quick revision summary

• Inside a prism r₁ + r₂ = A, and the deviation is δ = i + e − A.
• δ depends on i: it is least, D_m, when i = e (in an equilateral prism the ray inside then runs parallel to the base); other allowed transmitted deviations below the grazing-limit maximum occur at two angles of incidence.
• At minimum deviation r = A/2 and i = (A + D_m)/2, so n₂₁ = sin[(A + D_m)/2]/sin(A/2).
• A thin prism deviates light by D_m = (n₂₁ − 1)A, a small angle.

Questions students ask

What does the angle of deviation of a prism depend on?

The angle of deviation of a prism depends on the angle of incidence i, the prism angle A and the refractive index n₂₁ of the prism relative to its surroundings, which depends in turn on the colour of the light (NCERT pages 228 and 239). For a given i, a larger A or n₂₁ deviates the ray more, and the minimum deviation depends on A and n₂₁ alone (reasoned from NCERT Eqs. (9.34)–(9.38)). So a glass prism deviates violet light more than red, because its index is larger for violet (NCERT Science Class 10, Chapter 10, page 167; index and wavelength).

What is the difference between refraction through a prism and through a glass slab?

In a glass slab the two faces are parallel, so the bending at the second face undoes the bending at the first: the ray leaves parallel to the incident ray, shifted sideways but not deviated (the glass slab). In a prism the faces meet at the angle A, so the two refractions generally give a net turn towards the base, and it leaves deviated by δ = i + e − A (NCERT Eq. (9.35), page 239), as NCERT Science Class 10, Chapter 10 also notes (pages 165–166). And while a slab’s lateral shift grows with its thickness, a prism’s deviation is an angle set by A, n and i, whatever the prism’s size (reasoned).

Does a prism reflect or refract light?

A glass prism both reflects some light at its interfaces and refracts the transmitted part: a ray bends at the face it enters and again at the face it leaves, and comes out deviated towards the base (NCERT Section 9.6, page 239). A prism reflects when the ray meets the second face at more than the critical angle: then no light emerges there and the ray is totally reflected inside, which is how totally reflecting prisms bend light by 90° or by 180° (NCERT page 231). Which happens depends on the angle at which the ray meets that face, so the same prism can do either.

Is the deviation of a thin prism independent of the angle of incidence?

The deviation of a thin prism is nearly independent of the angle of incidence, but only while that angle is small: then the angles at both faces are small enough for sin θ ≈ θ, and the deviation stays close to (n₂₁ − 1)A (reasoned from NCERT Eqs. (9.34)–(9.35), page 239). For an 8° prism with n = 1.55, (n − 1)A = 4.40°, and Snell’s law at both faces gives 4.46° at normal incidence and 4.43° at i = 10°, but 5.09° at 30° and 5.88° at 40°. So the thin prism result of NCERT page 240 is used for rays near normal incidence.

Is dispersion by a prism deleted from Class 12 Physics?

Yes, dispersion of light by a prism is no longer a section of the 2026–27 NCERT Class 12 chapter: Section 9.6 ends with the thin prism (page 240), and dispersion appears only in passing, in the chapter’s introduction (page 222), Summary point 7 (page 247) and Points to Ponder 4, on the coloured images of thick lenses (page 248). Unit 16 of the JEE Main syllabus lists “refraction of light through a prism”, and NEET (UG) 2026 “Refraction of light through a prism.”, without naming dispersion. The splitting of white light by a prism and the rainbow are explained in NCERT Science Class 10, Chapter 10 (pages 166–167).

Practice questions

Try each question first, then open the answer to check your working.

1. Q1. At the angle of minimum deviation, how are i and e related, and what are r₁ and r₂?

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   i = e, and r₁ = r₂ = A/2 (NCERT Eq. (9.36), page 240).

2. Q2. A prism of angle 60° has a minimum deviation of 30°. Find its refractive index.

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   n = sin 45°/sin 30° = 0.707/0.5 ≈ 1.41 (NCERT Eq. (9.38), page 240).

3. Q3. Find the deviation produced by a thin prism of angle 5° and refractive index 1.6.

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   D_m = (1.6 − 1) × 5° = 3° (NCERT page 240).