Refraction through Prisms: NEB Class 11 Physics Guide

Curriculum boundary

What prism refraction includes

The CDC secondary curriculum includes minimum deviation, refractive index and deviation by a small-angle prism. Check the CDC Physics Grade 11 page for current Nepal resources.

Review OpenStax Snell’s law before treating two faces. The OpenStax refraction and prism overview connects refractive index with prism bending and dispersion.

Two boundaries

Name every prism angle

The apex angle A is between the two refracting faces. At face 1, incident angle i and internal refraction r₁ are measured from its normal. At face 2, internal angle r₂ and emergence angle e are measured from the second normal. Geometry inside gives A=r₁+r₂.

Deviation δ is the angle between the original incident direction extended and the emergent ray. It is not the emergence angle. For a prism in the usual orientation the net ray deviates toward the base.

Build the relation

Why δ=i+e−A

Deviation at face 1 is i−r₁, and at face 2 it is e−r₂. Adding gives δ=i+e−(r₁+r₂). Since r₁+r₂=A, δ=i+e−A.

Each surface still obeys Snell’s law. Use n_airsin i=n_prismsin r₁ and n_prismsin r₂=n_airsin e.

Symmetric path

Minimum deviation and refractive index

As incidence changes, deviation falls to a minimum then rises. At the minimum for a reversible prism path, i=e and r₁=r₂=A/2. From δ_m=2i−A, i=(A+δ_m)/2.

Apply Snell’s law at the first face for a prism in air: n=sin i/sin r₁=sin[(A+δ_m)/2]/sin(A/2).

Small-angle approximation

Thin-prism deviation

For small angles in radians, sinθ≈θ. With air outside, i≈nr₁ and e≈nr₂. Therefore δ=i+e−A≈n(r₁+r₂)−A=(n−1)A.

This approximation requires a small prism angle and small ray angles. Do not use degrees inside the mathematical small-angle approximation without understanding that the ratio is dimensionless; the familiar δ and A can share the same small angular unit for the final proportional form.

Colour dependence

Why a prism disperses white light

Refractive index varies with wavelength. In ordinary transparent glass, shorter visible wavelengths usually have a larger n and are deviated more than longer wavelengths. A prism therefore spreads white light into a spectrum.

Dispersion is not required to derive monochromatic minimum-deviation geometry, but measuring δ_m for different colours reveals n(λ). Use a narrow spectral source and safe laboratory procedure; never look into intense beams.

Mixed reasoning

More prism examples

Practical method

Find minimum deviation experimentally

Trace the prism, use a narrow ray or pin alignment and measure deviation for several incidence angles. Plot δ against i; the lowest region estimates δ_m. At the minimum, check approximate symmetry i≈e.

Keep the prism fixed, mark ray lines widely separated, draw normals accurately and repeat near the minimum with smaller incidence steps. A broad minimum makes one “lowest” reading uncertain, so use the curve and report a range.

Never look into a laser or intense source. Use teacher-approved apparatus and eye-safe alignment. PhET Bending Light can support one-boundary predictions before the two-face experiment.

Exam routine

Seven steps for prism problems

1. Draw prism, base and both normals.
2. Label i, r₁, r₂, e, A and δ.
3. Use r₁+r₂=A.
4. Use δ=i+e−A.
5. Apply Snell’s law at each face.
6. At minimum impose i=e and r₁=r₂.
7. Check direction and approximation.

Review plane refraction for Snell fluency and Physical Quantities for angle and unit checks. For online or physical NEB tuition, call 9846662070.

Practice tasks

Closed-book prism checkpoint

1. Label all prism angles.
2. Derive δ=i+e−A.
3. Explain minimum-deviation symmetry.
4. Derive the refractive-index relation.
5. Solve two δ_m questions.
6. Derive thin-prism deviation.
7. Explain dispersion.
8. Evaluate a minimum-deviation experiment.

References and next steps

Sources and related study guides

• CDC Nepal: Physics Grade 11
• CDC Nepal: Secondary Curriculum
• OpenStax: Snell Law
• OpenStax Physics: Refraction and Prisms
• OpenStax: Optics Problems
• OpenStax: Concept Questions
• PhET: Bending Light

Continue with the prism study guide for spaced derivation and experiment practice. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Reversibility and two paths

Why the same deviation can occur twice

For a deviation slightly above the minimum, the δ–i curve has two incidence values. The corresponding paths interchange incidence and emergence when the ray direction is reversed. This is optical reversibility, not two different prism laws.

At the minimum the two paths merge into the symmetric case. Connecting the graph to reversibility explains why i=e is physical evidence rather than an arbitrary shortcut.

Full two-face calculation

Trace a prism when the path is not at minimum deviation

Suppose a prism in air has A=60°, n=1.50 and incidence i=45°. At face 1, sin r₁=sin45°/1.50≈0.4714, so r₁≈28.1°. Geometry gives r₂=A−r₁≈31.9°. At face 2, sin e=1.50sin31.9°≈0.793, so e≈52.5°. Total deviation is δ=i+e−A≈37.5°.

Check that r₁+r₂=60° and that each refraction direction is sensible: air to glass bends toward the first normal; glass to air bends away from the second. Because i and e differ, this is not exactly the minimum-deviation path.

Compare with the minimum

For A=60° and n=1.50, minimum deviation satisfies sin[(60°+δ_m)/2]=1.50sin30°=0.75. Thus δ_m≈37.2°, close to but slightly below the calculated 37.5°. The chosen incidence was near the symmetric value.

Thin-prism dispersion

If n_violet=1.54 and n_red=1.51 for a small A=5°, deviations are about 2.70° and 2.55°. Angular dispersion is approximately 0.15°. These supplied indices are illustrative; real values depend on material and wavelength.

Deviation curve

Interpret the full incidence range

At very low or very high permitted incidence, the prism path is asymmetric and deviation is larger than its minimum. As i changes, the internal angles and emergence adjust together. The smooth minimum occurs when the path becomes symmetric.

For a deviation above δ_m, two incidence values may exist. Reversing one ray path interchanges incidence and emergence, showing optical reversibility. At δ_m the pair merges and i=e.

Applications with boundaries

Prisms can redirect beams, disperse wavelengths and fold optical paths. A right-angle prism can use total internal reflection under suitable index and incidence conditions; a dispersing prism uses wavelength-dependent refraction. Identify which phenomenon is doing the work instead of calling every prism effect “dispersion.”

In measurement, minimum deviation offers a stable symmetry condition for estimating refractive index, but result quality still depends on apex angle, wavelength, alignment and temperature.