Virtual laboratory/Physics/Optics/Refraction and reflection of light — Snell's law

Refraction and reflection of light — Snell's law

What we'll do: We'll aim a light ray at the boundary between two media (e.g. air–water) and watch how it refracts and reflects, and when it reflects completely.

What you see on screen: The boundary between two media with the normal, the incident, reflected and refracted rays, an angle-of-incidence slider and a medium switch (air/water/glass). The bar shows the Snell's-law relation. Readouts: the refractive indices, the angles of incidence and refraction, the critical angle and the state (refraction / total internal reflection).

Refraction and reflection of light — Snell's law
Physics · Optics · Snell's law (FIZ.FALE.PP.05)
Upper medium (n₁)
Lower medium (n₂)
Angle of incidence θ₁ (from the normal)40°
A ray passes from air into water — will it bend CLOSER to or FARTHER from the normal?
n₁
1.00
n₂
1.33
θ₁ incidence
40°
θ₂ refraction
28.9°
θ_c critical
—
state
Refraction
🎯 Challenge: tune the angle of incidence so the ray refracts at the given θ₂

What just happened?

Entering water (an optically denser medium), the ray refracted CLOSER to the normal. Going back out into air, it would bend farther away.

Law of refraction (Snell's law):

n1sin⁡θ1=n2sin⁡θ2n_1 \sin\theta_1 = n_2 \sin\theta_2

n is the refractive index of the medium. Entering a medium with larger n (optically denser), the ray bends toward the normal; into a medium with smaller n — away from the normal. The angle of reflection always equals the angle of incidence.

Critical angle and total internal reflection:

passing into a rarer medium, above a certain angle the ray does not refract at all — all of it returns inside.

sin⁡θc=n2n1\sin\theta_{c} = \dfrac{n_2}{n_1}

This effect powers optical fibres and makes the underside of a water surface behave like a mirror.

Why this matters for your exam:

Snell's law and computing angles and the critical angle are the basis of geometric-optics problems. The trick: write down n for both media and substitute into n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1 = n_2\sin\theta_2.

Remember: into a denser medium — closer to the normal, into a rarer one — farther; and above the critical angle light reflects completely.

Illustrative model · NexTutor Virtual laboratory

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Theory & formulas

Law of refraction (Snell's law)

At the boundary between two media: n1 sin⁡θ1=n2 sin⁡θ2n_1\,\sin\theta_1 = n_2\,\sin\theta_2 Entering an optically denser medium (larger nn), the ray refracts toward the normal; into a rarer one — away from the normal.

Law of reflection

The angle of reflection equals the angle of incidence (θrefl=θinc\theta_{refl} = \theta_{inc}).

Total internal reflection

Passing into a rarer medium above the critical angle, light does not refract at all — it reflects completely. The critical angle: sin⁡θc=n2n1(n1>n2)\sin\theta_{c} = \dfrac{n_2}{n_1}\qquad (n_1 > n_2)

Notation: n1, n2n_1,\ n_2 — refractive indices of the media, θ1\theta_1 — angle of incidence, θ2\theta_2 — angle of refraction, θc\theta_{c} — critical angle.

Frequently asked questions

›

What is Snell's law?

n₁·sinθ₁ = n₂·sinθ₂ — it relates the angles of incidence and refraction to the refractive indices of the media.

›

When does light refract toward the normal?

When it enters an optically denser medium (with larger n), e.g. from air into water.

›

What is total internal reflection?

Passing into a rarer medium above the critical angle, light does not refract but reflects completely (sinθ_c = n₂/n₁).

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Speed of EM waves in a medium — refraction →Dispersion of light in a prism →Converging lens — where will the image form? →Optical fibre →Gravitational lensing — the bending of light →Spherical mirrors — concave and convex →