Dispersion: NEB Class 11 Physics Guide

Curriculum boundary

What dispersion adds to prism refraction

The CDC secondary curriculum includes dispersion in geometrical optics; check the CDC Physics Grade 11 page for current Nepal resources. Review Refraction through Prisms before adding wavelength dependence.

The definitions and physical explanations here are cross-checked with OpenStax dispersion, rainbows and prisms and OpenStax University Physics dispersion.

Physical cause

Refractive index depends on wavelength

At a stationary boundary, frequency remains fixed while speed and wavelength change in the medium. The material’s refractive index n(λ) is not exactly the same for every wavelength. Snell’s law n₁sin i=n₂sin r therefore gives slightly different refraction angles to different spectral components entering the same prism.

For many transparent materials in the visible range under normal dispersion, n_violet>n_red. Violet slows more in the optical model and bends more toward the normal on entry, then more away from the normal on exit. The net prism deviation is therefore greater for violet than red. State “for ordinary visible-light glass” rather than treating this order as a universal law for every material and wavelength.

Prism geometry

From one deviation to a family of deviations

For a monochromatic ray through a prism, A=r₁+r₂ and δ=i+e−A. At minimum deviation, i=e and r₁=r₂=A/2, giving n=sin[(A+δ_m)/2]/sin(A/2) for a prism in air. White light needs one refractive index and one minimum deviation for each wavelength.

For a thin prism and small angles in radians, δ≈(n−1)A. Angular dispersion between violet and red is Δδ≈(n_v−n_r)A. This is an approximation, so do not use it uncritically for a large-angle prism.

Continuous spectrum

Colour labels sample a wavelength continuum

Red, orange, yellow, green, blue and violet are useful names, sometimes with indigo added, but a prism produces a continuous distribution rather than six or seven physically separated packets. Perceived colour also depends on the spectrum reaching the eye and the visual response.

Atmospheric application

A rainbow uses refraction, reflection and geometry

Sunlight entering a water droplet is refracted and dispersed, internally reflected, then refracted again as it exits. Different wavelengths leave a droplet at different directions. An observer receives a given colour from droplets positioned at the appropriate angle, so the visible arc is an angular selection from many droplets—not a coloured physical band at one fixed distance.

A primary rainbow and a laboratory prism both separate wavelengths, but their paths differ. Do not reduce the rainbow to “total internal reflection only”; entry and exit refraction plus internal reflection are all essential in the basic geometric model.

Optical consequence

Chromatic aberration is unwanted dispersion

A simple lens can have different focal lengths for different wavelengths because n varies with λ. White-light images may show coloured fringes or wavelength-dependent focus. Combining lens elements made from different glasses can reduce chromatic aberration over selected wavelengths, but no introductory correction should be described as perfect for all colours and field positions.

Dispersion is also useful: prisms and diffraction-based instruments separate spectra for material identification, astronomy and wavelength measurement. In communication media, wavelength-dependent group delay can broaden pulses. Always specify whether dispersion is helping measurement or limiting image or signal quality.

Practical investigation

Observe a spectrum safely and measure carefully

1. Use a teacher-approved white-light source and narrow slit; never look into a laser or intense beam.
2. Align the slit, prism and screen at a common height.
3. Rotate the prism to obtain a clear spectrum.
4. Mark red and violet extremes on paper without placing eyes in the beam.
5. Measure screen distance and colour separation to estimate angular spread for small angles.
6. Repeat after realignment and report uncertainty from band width and position judgement.

A broader slit increases brightness but makes each wavelength’s image wider, reducing separation clarity. Ambient light lowers contrast. Prism material, apex angle, source spectrum, screen distance and alignment all affect the observation. Use PhET Bending Light to review wavelength-sensitive refraction after making a prediction.

Worked reasoning

Derive, calculate and interpret

Common mistakes and repair

• Calling the spectrum seven discrete wavelengths: state that it is continuous.
• Saying frequency changes at entry: frequency is fixed by the source and boundary continuity.
• Using thin-prism equations without a small-angle statement.
• Confusing dispersion with scattering or diffraction: identify the wavelength-dependent mechanism.
• Describing a rainbow with refraction alone: include internal reflection and observer geometry.
• Using exact-looking glass indices without stating that material and wavelength determine them.

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References and next steps

Sources and related study guides

• CDC Nepal: Physics Grade 11
• CDC Nepal: Secondary Curriculum
• OpenStax: Dispersion, Rainbow and Prisms
• OpenStax University Physics: Dispersion
• OpenStax: Refraction
• PhET: Bending Light

Continue with the Dispersion Study Guide and compare chromatic focus with the Lenses guide. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Mechanism comparison

Separate dispersion, diffraction and scattering

All three can produce colour-dependent observations, but the causal model, geometry and equations differ. A diffraction grating can separate wavelengths without relying on refractive-index variation. Atmospheric colour cannot be explained by saying “air acts like a prism” in every situation.

Recombination test

Place a second identical prism with opposite orientation after the first spectrum and align it so wavelength-dependent deviations are reversed. The emerging components can overlap into a near-white beam. This demonstrates that the first prism separated existing components; it did not permanently change them into new substances.

Resolution versus dispersion

A larger angular spread can help separate nearby wavelengths, but a spectrometer’s ability to resolve them also depends on slit width, aberration, detector sampling, diffraction and signal quality. Do not equate “more colourful” with automatically more precise measurement.

In an exam comparison, state the controlling wavelength dependence first, draw the geometry second, then name the observation. This ordering prevents rainbow, prism, grating and blue-sky explanations from collapsing into one vague statement.