Pick your class, read the steps, then try them right in the lab —
change one slider at a time and watch the rays and graphs respond.
Class 10 — Refraction and the refractive index
Concept: light changes direction when it passes from one medium into another because its speed changes.
Snell's law connects the angles: n1 sinθ1 = n2 sinθ2, and
n = c ÷ v.
- Open Snell's law & TIR. Choose Air (n = 1.00) above, Glass (n = 1.50) below, and set the angle of
incidence to 40°. sinθ2 = sin 40° ÷ 1.5 = 0.4285, so θ2 = 25.4°:
the ray bends towards the normal.
- Light travels at 300 × 106 m/s in air but only 300 ÷ 1.5 = 199.9 × 106 m/s in
glass. Watch the two moving dots: the one in the glass is slower.
- Change the lower medium to Diamond (n = 2.42): θ2 falls to 15.4°. The denser the medium, the
more the ray bends towards the normal.
- Now put Glass above and Air below, with i = 20°: sinθ2 = 1.5 × sin 20°, so
θ2 = 30.9°. Going into a rarer medium the ray bends away from the normal.
Takeaway: into a denser medium the ray bends towards the normal, into a rarer medium away from it;
the frequency does not change, the speed and the wavelength do.
Class 12 — Total internal reflection and the critical angle
Concept: going from a denser to a rarer medium, the refracted ray bends away from the normal. At the
critical angle θc it would run along the surface; beyond that there is no refracted ray at all
and all the light is reflected: sinθc = n2 ÷ n1.
- Set Glass (1.50) above and Air (1.00) below. sinθc = 1 ÷ 1.5 = 0.667, so
θc = 41.8°. A dashed red line on the stage marks this angle.
- At i = 40° there is still a refracted ray, bent almost along the surface (θ2 = 74.6°).
At i = 42° it vanishes: total internal reflection.
- On the lower graph the reflected share climbs to 100% at the critical angle and stays there.
- Try water (1.33): θc = 48.8°. Diamond (2.42): only 24.4°, so most rays inside a cut diamond are
totally reflected, which is why it sparkles.
- Total internal reflection needs both conditions: dense to rare, and an angle beyond the critical angle.
Takeaway: the larger the refractive index, the smaller the critical angle.
Class 10 — A glass slab and apparent depth
Concept: a ray crossing a parallel-sided slab is refracted twice and comes out parallel to its original
direction but shifted sideways. An object under water looks nearer the surface than it is.
- Open Slab & apparent depth with n = 1.50, t = 4 cm, i = 45°. The ray bends to r = 28.1° inside and
leaves at 45° again: it is parallel to the incident ray.
- The lateral shift is d = t sin(i − r) ÷ cos r = 4 × sin 16.9° ÷ cos 28.1° = 1.32 cm.
A 6 cm slab shifts it by 1.97 cm; at normal incidence (i = 0°) the shift is zero.
- Switch to Apparent depth: n = 1.33 and a coin 6 cm deep. Looking straight down it appears at
6 ÷ 1.33 = 4.51 cm, about a quarter shallower than the real depth.
- Raise n to 2.0: the coin appears only half as deep. A denser liquid looks shallower.
Takeaway: apparent depth = real depth ÷ n; the emergent ray from a slab is parallel to the
incident ray.
Class 12 — The prism and minimum deviation
Concept: a ray is refracted at both faces of a prism, so it is bent towards the base. The angles inside obey
r1 + r2 = A, and the deviation is δ = i + e − A.
- Open Prism & dispersion: crown glass (n = 1.517 for yellow), A = 60°, i = 50°, and tick
“one colour” if you wish. r1 = 30.3°, r2 = 60° − 30.3° = 29.7°,
sin e = 1.517 × sin 29.7°, so e = 48.7°.
- The deviation is δ = 50° + 48.7° − 60° = 38.7°.
- Move the angle of incidence. At i = 30° the deviation is larger (52.0°); at i = 70° it is 44.2°;
near i = 49° it is smallest. The left graph is U-shaped.
- At the minimum, i = e and the ray inside is parallel to the base:
δmin = 2 sin−1(n sin 30°) − 60° = 38.66° at i = 49.33°. Rearranged,
n = sin((A + δmin) ÷ 2) ÷ sin(A ÷ 2): the way n is measured.
- Choose Dense flint glass, A = 70°, i = 20°: the ray reaches the second face at an angle larger than the
critical angle and is totally reflected; no ray comes out.
Takeaway: δ = i + e − A, with a minimum when the ray passes symmetrically through the prism.
Class 12 — Dispersion of white light
Concept: the refractive index of glass is slightly larger for violet than for red, so a prism bends the
colours by different amounts and spreads white light into a spectrum.
- In Prism & dispersion keep crown glass, A = 60°, i = 50°, white light on. The index is 1.530 for violet
(410 nm), 1.517 for yellow and 1.514 for red (680 nm). The stage magnifies the spreading ×5 so you can see it; the
graphs and explanation show the true values.
- Violet is deviated by 39.82° and red by 38.41°: an angular dispersion of 1.41°. On the right-hand graph
the deviation falls steadily as the wavelength grows.
- The dispersive power is ω = (nF − nC) ÷ (nd − 1) =
(1.5227 − 1.5146) ÷ 0.517 = 0.0157 (Abbe number 64).
- Switch to flint glass: the deviations are 51.64° (violet) and 47.87° (red), and ω = 0.0275. Flint
disperses almost twice as strongly as crown.
Takeaway: dispersion happens because n depends on the wavelength; flint glass has a larger dispersive power
than crown glass.
Class 12 — The optical fibre and the acceptance angle
Concept: an optical fibre has a core of higher index n1 inside a cladding of lower index
n2. Light that hits the wall at more than the critical angle is totally reflected again and again and
follows the fibre.
- Open Optical fibre with n1 = 1.50, n2 = 1.45. The critical angle at the wall is
sin−1(1.45 ÷ 1.50) = 75.2°.
- The largest angle at which light can enter from air is given by
sinαmax = √(n1² − n2²) = √(2.25 − 2.1025) = 0.384, so
αmax = 22.6°. The red dashed lines show this acceptance cone.
- Enter at 15°: inside the glass the ray makes 9.9° with the axis and meets the wall at 80.1° > 75.2°, so it is
guided. With a 1 mm core it is reflected 175 times per metre.
- Enter at 35°, outside the cone: the ray meets the wall at less than the critical angle and leaks into the
cladding.
- Raise n2 towards n1: the acceptance cone shrinks; widen the gap and it grows.
Takeaway: NA = √(n1² − n2²); steeper guided rays travel further and arrive
later (modal dispersion).
Class 12 — The lens-maker's formula and spherical aberration
Concept: a lens focuses light because both of its curved faces refract it. Its focal length follows from the
glass and the shape: 1 ÷ f = (n ÷ nm − 1)(1 ÷ R1 − 1 ÷ R2).
- Open Lens-maker & ray tracing with a biconvex lens, n = 1.50 and both radii 30 cm. In air,
1 ÷ f = 0.5 × (1 ÷ 30 + 1 ÷ 30), so f = 30 cm (a power of 3.33 dioptres). The rays meet near the
marked F.
- Change the shape to plano-convex (one flat face): f = 60 cm. Biconcave gives f = −30 cm: a diverging lens.
- Put the biconvex lens in water (nm = 1.33): the relative index is 1.5 ÷ 1.33 = 1.128 and the focal length grows
to 117.4 cm. In a liquid of index 1.50 it would have no power at all.
- The formula is for rays near the axis. Set the beam height to 4 cm: that ray crosses at 29.5 cm but a ray 0.2 cm from
the axis crosses at 30.4 cm. The outer rays focus closer: spherical aberration.
- Raise n to 2.0 and watch the focal length fall (f ∝ 1 ÷ (n − 1)).
Takeaway: a lens needs a higher index than its surroundings to converge light; its power is the sum of
what each curved surface contributes.