Preview

Bending Light

Q: Light goes from glass (n=1.5) to air (n=1.0) at 45°. What is the refraction angle?

You can work it out this way: apply Snell's Law: 1.5×sin(45°) = 1.0×sin(θ₂).

Q: Find the critical angle for glass (n=1.5) to air.

Θ_c = arcsin(n₂/n₁) = arcsin(1/1.5).

Q: Why does a diamond sparkle more than glass?

You can work it out this way: compare their indices of refraction and critical angles.

Explore refraction, reflection, and Snell's Law

A straw in a glass of water looks broken at the surface — your brain insists the light traveled straight to your eye, and the straw betrays it. The truth is stranger: light never bends mid-medium. It kinks only at the border, because a wave whose speed drops from c to c/n must swing its direction to keep its crests continuous across the line. In this lab you hold that border in your hands. A blue incident ray strikes the interface, a green refracted ray carries the light onward, and an amber reflected ray — the one nobody expects — is always there, quietly sharing the energy. Push the beam from air into water or glass and Snell's law pins every angle to the tenth of a degree. Then flip the world: fire from inside the glass outward, raise the angle past 41.8°, and the green ray does not bend away — it ceases to exist. Every photon turns back. That vanishing act threads the internet through fiber optics and makes a diamond outsparkle glass.

What you'll be able to do

Apply Snell's law n₁sinθ₁ = n₂sinθ₂ to predict the refracted angle at any interface, and state the bend direction from the indices alone: toward the normal entering a denser medium (n₂ > n₁), away entering a rarer one
State the two conditions for total internal reflection (n₁ > n₂ and θ₁ > θ_c = arcsin(n₂/n₁)) and explain what physically happens past the critical angle: the transmitted ray ceases to exist — Snell's law has no real solution — and all light reflects back into the denser medium
Explain refraction mechanistically through n = c/v: the wave's speed changes at the boundary while its frequency stays fixed, and phase continuity of the wavefront across the interface forces the direction change — the ray does not 'choose' to bend

Formulas

n_1 \sin\theta_1 = n_2 \sin\theta_2

Snell's Law

\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)

Critical angle (TIR)

n = \frac{c}{v}

Index of refraction

Make a prediction

Load the Total Internal Reflection preset: the laser fires from inside glass (n₁ = 1.50) toward air (n₂ = 1.00), whose critical angle the panel shows as θ_c = 41.8°. The incident angle starts at 40° — the green refracted ray grazes out at θ₂ ≈ 74.6° — and you drag it up to 55°. What happens to the light?

No grading here — commit to a guess, then scroll down and test it yourself.

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Explore

Hit the Air→Water preset and read the Live Data panel: θ₁ = 30.0°, θ₂ = 22.1°, θ_c = N/A — no critical angle exists while n₁ < n₂. Now drag n₂ from 1.33 down to 1.00 and watch θ₂ climb back to 30.0°: with matched media the ray goes straight through and the green and blue rays line up.
Hit the Air→Glass preset (θ₁ = 35°, θ₂ = 22.5°), then sweep the incident angle slider the full 0 → 89°. θ₂ rises from 0.0° but caps at 41.8° — air-to-glass refraction can never exceed the glass-air critical angle. Snell's law is reciprocal: the ceiling you just hit is the cliff edge of the next station.
Hit the Total Internal Reflection preset (glass→air, θ₁ = 55° > θ_c = 41.8°): the green refracted ray is gone, d-t2 reads '—', the status row has flipped to Total Internal Reflection, and the amber reflected ray burns at full brightness. Now drag the incident angle down slowly — the green ray flickers back to life between 42° and 41°, grazing the surface at θ₂ ≈ 79.8°.
Back on Air→Glass: set the incident angle to 20° and read θ₂ ≈ 13.2°, then set 40° and read θ₂ ≈ 25.4°. You doubled the incident angle but the refracted angle grew by less than double — arcsin is not linear, and the panel proves it (the same pair the sim's quiz Q3 computes).

Scroll for the debrief ↓

Check

Did the lab agree with you?

Your prediction

You skipped the prediction — jump back to the preview and commit to a guess first; the comparison is the whole point.

Answer: The green refracted ray vanishes entirely — d-t2 flips to '—' — and every photon reflects back into the glass; the amber reflected ray jumps to full brightness

Snell's law decides this, and past 41.8° it has nothing to say: sinθ₂ = n₁·sinθ₁/n₂ = 1.5·sin55° = 1.229, and no real angle has a sine greater than 1. There is no transmitted solution — not a dim one, not a straightened one, none. The engine (computeSnell) sets t2 = null, the green ray's visible flag drops, d-t2 flips to '—', the status row reads Total Internal Reflection, and the amber reflected ray goes from 0.4 to full opacity: every photon turns back into the glass. At 40° the law still had an answer — θ₂ = asin(1.5·sin40°) = asin(0.964) = 74.6° — which is why the crossover on the integer slider is so sharp: at 41° the ray still grazes out at 79.8°, at 42° (1.5·sin42° = 1.0037 > 1) it is gone. Option B is the targeted misconception — the intuition that a ray must continue somewhere. But 'total' internal reflection is total: this is the physics that keeps light inside fiber-optic cables, and the panel's θ_c = 41.8° (asin(1/1.5), the same value the sim's quiz Q2 computes) marks the exact border where transmission ends.

Quiz (0/3)

Light goes from glass (n=1.5) to air (n=1.0) at 45°. What is the refraction angle?

Find the critical angle for glass (n=1.5) to air.

Why does a diamond sparkle more than glass?

You can now

Apply Snell's law n₁sinθ₁ = n₂sinθ₂ to predict the refracted angle at any interface, and state the bend direction from the indices alone: toward the normal entering a denser medium (n₂ > n₁), away entering a rarer one
State the two conditions for total internal reflection (n₁ > n₂ and θ₁ > θ_c = arcsin(n₂/n₁)) and explain what physically happens past the critical angle: the transmitted ray ceases to exist — Snell's law has no real solution — and all light reflects back into the denser medium
Explain refraction mechanistically through n = c/v: the wave's speed changes at the boundary while its frequency stays fixed, and phase continuity of the wavefront across the interface forces the direction change — the ray does not 'choose' to bend