Snell's Law Calculator

Calculate the refraction of light between two media using Snell's Law. Perfect for students, engineers, and physics enthusiasts.

Full original guide (expanded)

Snell's Law Calculator

Compute refraction angles with Snell’s law using indices of refraction and incident angle.

Calculator

Results

Angle of Refraction (degrees): -

Data Source and Methodology

All calculations are based on Snell's Law as formulated in standard physics literature. For further details, refer to the Wikipedia article on Snell's Law. All calculations adhere strictly to these formulas.

The Formula Explained

\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]

Where \( n_1 \) and \( n_2 \) are the refractive indices of medium 1 and medium 2, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction, respectively.

Glossary of Variables

  • Angle of Incidence (\( \theta_1 \)): The angle between the incident ray and the normal to the surface at the point of incidence.
  • Index of Refraction (\( n_1, n_2 \)): A measure of how much the speed of light is reduced inside a medium.
  • Angle of Refraction (\( \theta_2 \)): The angle between the refracted ray and the normal to the surface.

How It Works: A Step-by-Step Example

Consider a light ray entering water from air. If the angle of incidence is 30°, and the refractive index of air is 1.0 and that of water is 1.33, the angle of refraction can be calculated using Snell's Law:

\[ 1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2) \]

Solving for \( \theta_2 \), you find the angle of refraction to be approximately 22.09°.

Frequently Asked Questions (FAQ)

What is Snell's Law?

Snell's Law relates the angles of incidence and refraction to the refractive indices of the two media involved.

How do I calculate the angle of refraction?

Use the formula \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \) and solve for \( \theta_2 \).

What are refractive indices?

Refractive indices are numbers that describe how light propagates through a medium. The higher the index, the slower light travels in that medium.

Can Snell's Law be applied to any light wave?

Yes, Snell's Law can be applied to any type of light wave, including visible light, microwaves, and radio waves.

What happens if the angle of incidence is zero?

If the angle of incidence is zero, the light travels perpendicular to the boundary, and there is no refraction; the angle of refraction is also zero.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[n_1 \sin(\theta_1) = n_2 \sin(\theta_2)\]
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
Formula (extracted LaTeX)
\[1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2)\]
1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2)
Formula (extracted text)
\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Snell's Law Calculator

Compute refraction angles with Snell’s law using indices of refraction and incident angle.

Calculator

Results

Angle of Refraction (degrees): -

Data Source and Methodology

All calculations are based on Snell's Law as formulated in standard physics literature. For further details, refer to the Wikipedia article on Snell's Law. All calculations adhere strictly to these formulas.

The Formula Explained

\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]

Where \( n_1 \) and \( n_2 \) are the refractive indices of medium 1 and medium 2, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction, respectively.

Glossary of Variables

  • Angle of Incidence (\( \theta_1 \)): The angle between the incident ray and the normal to the surface at the point of incidence.
  • Index of Refraction (\( n_1, n_2 \)): A measure of how much the speed of light is reduced inside a medium.
  • Angle of Refraction (\( \theta_2 \)): The angle between the refracted ray and the normal to the surface.

How It Works: A Step-by-Step Example

Consider a light ray entering water from air. If the angle of incidence is 30°, and the refractive index of air is 1.0 and that of water is 1.33, the angle of refraction can be calculated using Snell's Law:

\[ 1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2) \]

Solving for \( \theta_2 \), you find the angle of refraction to be approximately 22.09°.

Frequently Asked Questions (FAQ)

What is Snell's Law?

Snell's Law relates the angles of incidence and refraction to the refractive indices of the two media involved.

How do I calculate the angle of refraction?

Use the formula \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \) and solve for \( \theta_2 \).

What are refractive indices?

Refractive indices are numbers that describe how light propagates through a medium. The higher the index, the slower light travels in that medium.

Can Snell's Law be applied to any light wave?

Yes, Snell's Law can be applied to any type of light wave, including visible light, microwaves, and radio waves.

What happens if the angle of incidence is zero?

If the angle of incidence is zero, the light travels perpendicular to the boundary, and there is no refraction; the angle of refraction is also zero.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[n_1 \sin(\theta_1) = n_2 \sin(\theta_2)\]
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
Formula (extracted LaTeX)
\[1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2)\]
1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2)
Formula (extracted text)
\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn

Snell's Law Calculator

Compute refraction angles with Snell’s law using indices of refraction and incident angle.

Calculator

Results

Angle of Refraction (degrees): -

Data Source and Methodology

All calculations are based on Snell's Law as formulated in standard physics literature. For further details, refer to the Wikipedia article on Snell's Law. All calculations adhere strictly to these formulas.

The Formula Explained

\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]

Where \( n_1 \) and \( n_2 \) are the refractive indices of medium 1 and medium 2, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction, respectively.

Glossary of Variables

  • Angle of Incidence (\( \theta_1 \)): The angle between the incident ray and the normal to the surface at the point of incidence.
  • Index of Refraction (\( n_1, n_2 \)): A measure of how much the speed of light is reduced inside a medium.
  • Angle of Refraction (\( \theta_2 \)): The angle between the refracted ray and the normal to the surface.

How It Works: A Step-by-Step Example

Consider a light ray entering water from air. If the angle of incidence is 30°, and the refractive index of air is 1.0 and that of water is 1.33, the angle of refraction can be calculated using Snell's Law:

\[ 1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2) \]

Solving for \( \theta_2 \), you find the angle of refraction to be approximately 22.09°.

Frequently Asked Questions (FAQ)

What is Snell's Law?

Snell's Law relates the angles of incidence and refraction to the refractive indices of the two media involved.

How do I calculate the angle of refraction?

Use the formula \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \) and solve for \( \theta_2 \).

What are refractive indices?

Refractive indices are numbers that describe how light propagates through a medium. The higher the index, the slower light travels in that medium.

Can Snell's Law be applied to any light wave?

Yes, Snell's Law can be applied to any type of light wave, including visible light, microwaves, and radio waves.

What happens if the angle of incidence is zero?

If the angle of incidence is zero, the light travels perpendicular to the boundary, and there is no refraction; the angle of refraction is also zero.


Audit: Complete
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
\[','\]
','
Formula (extracted LaTeX)
\[n_1 \sin(\theta_1) = n_2 \sin(\theta_2)\]
n_1 \sin(\theta_1) = n_2 \sin(\theta_2)
Formula (extracted LaTeX)
\[1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2)\]
1.0 \times \sin(30^\circ) = 1.33 \times \sin(\theta_2)
Formula (extracted text)
\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]
Variables and units
  • No variables provided in audit spec.
Sources (authoritative):
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
  • Initial audit spec draft generated from HTML extraction (review required).
  • Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
  • Confirm sources are authoritative and relevant to the calculator methodology.
Verified by Ugo Candido on 2026-01-19
Profile · LinkedIn
Formulas

(Formulas preserved from original page content, if present.)

Version 0.1.0-draft
Citations

Add authoritative sources relevant to this calculator (standards bodies, manuals, official docs).

Changelog
  • 0.1.0-draft — 2026-01-19: Initial draft (review required).