Physic Labs

Optics

Refraction of light, refractive index

Measure the refraction angle at a boundary between two media for several incidence angles and refractive indices. Verify Snell's law n1sin⁡i=n2sin⁡rn_1\sin i=n_2\sin r and the condition for total internal reflection.

Middle school

⚠ In real experiments with laser beams, never aim them at eyes and beware unexpected reflections from glass surfaces.

Equipment

  • 3D model of a light ray crossing the interface of two transparent media
  • Incidence-angle, refractive-index and focal sliders
  • Virtual protractor reading incidence and refraction angles from the normal

Procedure

  1. Vary the incidence angle at fixed index

    In panel 1, hold «Refractive index» at 1.5 and drag «Incidence angle» from 5° to 80°. Record the (i, r) pairs from the readouts; the refracted ray bends toward the normal entering the denser medium. Compute sin i / sin r for each pair and note it stays nearly constant.

  2. Verify Snell's law

    For three values of n₂ (e.g. 1.0, 1.5, 2.0), hold the incidence at 35° and read the refraction angle r. Check n1sin⁡i=n2sin⁡rn_1\sin i=n_2\sin r with n₁ = 1 (air): as n₂ grows, r shrinks — the ray bends harder toward the normal.

  3. Find the critical angle

    Reverse the direction (from high to low index), then raise the incidence until the refracted ray vanishes and only the reflected ray remains. Read that incidence and compare it with the critical angle sin⁡ic=n2/n1\sin i_c=n_2/n_1.

  4. Explore the focal slider in panel 2

    In panel 2, vary «Focal length» and watch the rays converge or diverge after the interface. Relate: higher index at the same curvature means stronger convergence — the premise of thin lenses; predict the bend before moving the slider, then check.

Simulation

Experiment history

The relation between incidence and refraction angles was pursued by seventeenth-century mathematicians well before its modern naming. Willebrord Snellius found the sine form around 1621 through measurement but never published; René Descartes put the formula into Dioptrique (1637) without a convincing derivation. Pierre de Fermat then derived the law from a least-time principle in 1657–1662 — among the first variational principles in physics. Snell's law n₁ sin i = n₂ sin r implies light travels slower in a refractive medium, which Hippolyte Fizeau measured directly in 1850 with a rotating toothed wheel. Augustin Fresnel, and later Maxwell, embedded refraction in wave theory: the index reflects the phase speed v=c/nv=c/n, and electromagnetism also explains total internal reflection — the phenomenon now at the core of optical fibers.

Related physicists

Isaac NewtonJames Clerk Maxwell

Related library topics

Refraction of light, refractive index