Opticsn₁ sinθ₁ = n₂ sinθ₂

Snell's Law Refraction Simulator

Visualize light refraction and total internal reflection. Adjust incidence angle and refractive indices to see Snell's law in action.

Parameters

Incidence angle θ₁

n₁ (medium 1)

n₂ (medium 2)

Wavelength λ

Computed

θ₂ (refraction)28.9°

Critical angle θ_cn/a (n₁ ≤ n₂)

Speed in n₁300 Mm/s

Speed in n₂226 Mm/s

θ₁40 °

θ₂28.9 °

θ_c0.0 °

n₁1.00

n₂1.33

λ780 nm

About Snell's Law

When light passes from one transparent medium into another, it changes direction at the interface. This bending of light is called refraction and is governed by Snell's Law, which relates the angles of incidence and refraction to the refractive indices of the two media.

ℹLight bends toward the normal when entering a denser medium (n₂ > n₁) and away from the normal when entering a less dense medium (n₂ < n₁).

Key Variables

Symbol	Name	Description
n₁	Refractive index (medium 1)	Speed of light ratio in medium 1 (n = c/v)
n₂	Refractive index (medium 2)	Speed of light ratio in medium 2
θ₁	Angle of incidence	Angle between incoming ray and the normal
θ₂	Angle of refraction	Angle between refracted ray and the normal
θ_c	Critical angle	Angle beyond which total internal reflection occurs
v	Phase velocity	Speed of light in medium (v = c/n)

Common Refractive Indices

Medium	n (approximate)
Vacuum / Air	1.00
Water (20°C)	1.33
Crown glass	1.52
Dense flint glass	1.70
Diamond	2.42

Total Internal Reflection

When light travels from a denser medium to a less dense medium (n₁ > n₂), and the incidence angle exceeds the critical angle θ_c, refraction is impossible — all light reflects back. This is called total internal reflection (TIR).

TIR is used in: optical fibres (telecommunications), diamond cutting (brilliance), binoculars (prisms), and reflectors.

💡Set n₁ = 1.52 (glass) and n₂ = 1.00 (air), then slowly increase θ₁. You will see refraction disappear above the critical angle (~41°) — total internal reflection.

Worked Example

Light travels from air (n₁ = 1.00) into water (n₂ = 1.33) at 40° incidence:

sin θ_{2} = \frac{n _{1}}{n _{2}} sin θ_{1} = \frac{1.00}{1.33} sin 40° = 0.484

θ_{2} = arcsin (0.484) \approx 28.9°

Key Formulas

Snell's Law

n_{1} sin θ_{1} = n_{2} sin θ_{2}

Refraction Angle

θ_{2} = arcsin (\frac{n _{1}}{n _{2}} sin θ_{1})

Critical Angle (when n₁ > n₂)

θ_{c} = arcsin (\frac{n _{2}}{n _{1}})

Speed of Light in Medium

v = \frac{c}{n} c = 3 \times 1 0^{8} m/s

Formula	Description	Notes
n₁ sin θ₁ = n₂ sin θ₂	Snell's Law	Conserved at any interface
θ₂ = arcsin(n₁/n₂ · sin θ₁)	Refraction angle	Undefined when n₁/n₂ · sin θ₁ > 1 (TIR)
θ_c = arcsin(n₂/n₁)	Critical angle	Only exists when n₁ > n₂
n = c/v	Refractive index definition	Always ≥ 1 for real media
Law of reflection: θᵢ = θᵣ	Reflection	Incidence = reflection angle

Frequently Asked Questions

Why does light bend when it enters a new medium?

Light slows down when entering a denser medium (higher n). Like a marching band turning when one side slows down first, the wavefront changes direction. The ratio of speeds determines the bending angle via Snell's Law.

Why can total internal reflection only happen from denser to less dense media?

TIR requires n₁ > n₂ so that sinθ₂ = (n₁/n₂)sinθ₁ can exceed 1. When n₁ ≤ n₂, (n₁/n₂) ≤ 1 so sinθ₂ is always ≤ 1 and a refracted ray always exists.

How do optical fibres use total internal reflection?

The glass core has a higher refractive index than the surrounding cladding. Light enters at a shallow angle, hitting the core-cladding interface beyond the critical angle. It reflects internally and travels along the fibre without leaking out.

What is the refractive index of vacuum?

Exactly 1.000000 by definition. All other media have n > 1 because light slows down relative to vacuum speed c = 299,792,458 m/s.

Does Snell's Law apply to sound waves?

Yes — any wave refraction follows the same relationship. For sound, n is replaced by the ratio of wave speeds v₁/v₂. Snell's Law is a universal wave property.