Refraction Through a Prism: Dispersion, Deviation, Spectra

A prism is a transparent wedge of glass with triangular cross-section. Light entering one face bends, travels inside, and bends again on exit. The total bending is called deviation, and because refractive index depends on colour, white light splits into spectrum — dispersion.

Prisms reveal the hidden colours in sunlight, form rainbows in labs, and are used in spectroscopes to analyse light from stars and chemicals. The prism is both a bending device and a colour separator.

Key Concepts

Prism angle A: Angle between two refracting faces, typically 60 degrees for equilateral glass prism.

Angle of deviation D: Total angle between incident ray direction and emergent ray direction, in degrees. Depends on incidence angle and material.

Dispersion: Splitting of white light into colours because n varies with wavelength: violet bends most (higher n), red least.

• Base is thick side opposite apex
• Deviation is toward base
• Spectrum order from base: violet closest to base, red farthest

Formulas

D = i1 + i2 minus A, where i1 incidence at first face, i2 emergence angle at second, A prism angle. Also internal refraction angles r1 + r2 = A. All angles in degrees.

Snell at each face: sin i1 divided by sin r1 = n, sin i2 divided by sin r2 = n for prism in air.

Minimum deviation Dm: n = sin((A + Dm) divided by 2) divided by sin(A divided by 2). This precise formula measures n. Assumes prism in air, monochromatic light.

Worked Example

Equilateral prism A = 60 degrees, n = 1.52 for yellow light. Find minimum deviation.

1. Use n = sin((A + Dm) divided by 2) divided by sin(A divided by 2).
2. sin(A divided by 2) = sin 30 degrees = 0.5.
3. So sin((60 + Dm) divided by 2) = n times 0.5 = 1.52 times 0.5 = 0.76.
4. (60 + Dm) divided by 2 = arcsin 0.76 = 49.46 degrees.
5. 60 + Dm = 98.92, Dm = 38.92 degrees approx 38.9 degrees.

At this symmetric position incident and emergent angles equal, ray inside parallel to base. Different colours give slightly different Dm, creating spread.

Common Misconceptions

• Prism creates colours: Colours already present in white light. Prism only separates them by different bending.
• Deviation always same: Deviation varies with incidence angle, has a minimum Dm. At other angles deviation larger.
• Red bends most: Violet has higher n, shorter wavelength, bends most toward base. Red bends least.

Real-World Applications

• Spectroscopes analyse element fingerprints from spectrum lines for chemistry and astronomy
• Prism in binoculars folds light path and corrects orientation using total internal reflection
• Rainbow is natural dispersion by water droplets acting like prisms
• Optical instruments measure refractive index accurately by minimum deviation method

Prism refracts twice, deviates light toward base, and disperses white into spectrum. Angle relations and minimum deviation formula unlock both measurement and colour science.