Snell's Law Calculator | Online Free Tool | Elysia Tools
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Snell's Law Calculator
n₁·sinθ₁ = n₂·sinθ₂ for either angle, with the total-internal-reflection regime and critical angle when sinθ exceeds 1.
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Tool usage guide
Learn when to use this tool, what it supports, and how real users apply it.
Key facts
Category
Science & Education
Input types
select, number
Output type
text
Sample coverage
4
API ready
Yes
Overview
The Snell's Law Calculator computes the angle of refraction or incidence for light traveling between two optical media using the relationship n₁·sinθ₁ = n₂·sinθ₂. It determines ray deviation relative to the surface normal and identifies total internal reflection boundaries along with the corresponding critical angle.
When to use
Determining the refracted angle of a light beam crossing an interface between two optical materials.
Back-calculating the required angle of incidence needed to achieve a target exit angle.
Evaluating whether an incident ray entering a rarer medium exceeds the critical angle and undergoes total internal reflection.
How it works
1Select whether to solve for the refraction angle (θ₂) or the incidence angle (θ₁).
2Enter the refractive indices for the incident medium (n₁) and the refracted medium (n₂).
3Specify the known angle value in degrees.
4The calculator applies Snell's law to yield the resulting angle, ray bending behavior, and any critical angle thresholds.
Use cases
Verifying theoretical refraction angles and critical limits for physics laboratory coursework.
Calculating ray deflection angles across air-glass boundaries in lens and prism configurations.
Assessing core-to-cladding boundary conditions and internal reflection thresholds in optical fiber systems.
Examples
1. Air to Glass Refraction Analysis
Physics Student
Background
A student is analyzing how a collimated light beam refracts when passing from ambient air into a crown glass block during an optics experiment.
Problem
Calculate the refracted angle inside the glass when light strikes the interface at an incident angle of 30°.
How to use
Set 'Solve for' to θ₂, enter n₁ = 1.0 (air), n₂ = 1.5 (glass), and input 30 for the given angle.
Outcome
The calculator outputs a refraction angle of 19.47° and indicates that the ray bends toward the normal as it enters the denser medium.
2. Glass to Air Exit Angle and Critical Limit
Optical Technician
Background
A technician is assessing ray exit behavior and total internal reflection limits when light passes out of a glass prism into air.
Problem
Determine the exit angle for a 30° internal ray and find the critical angle boundary for the glass-to-air interface.
How to use
Set 'Solve for' to θ₂, set n₁ = 1.5, n₂ = 1.0, and enter 30 for the given angle.
Outcome
FAQ
What is Snell's Law?
Snell's Law describes light refraction at an interface using the formula n₁·sinθ₁ = n₂·sinθ₂, where n represents the refractive index and θ represents the angle to the normal.
What happens when light exceeds the critical angle?
When light passes from a higher to a lower refractive index (n₁ > n₂) and sinθ₂ exceeds 1, refraction cannot occur and total internal reflection takes place.
Can I calculate the incident angle instead of the refracted angle?
Yes, choose 'Incidence angle θ₁' under the 'Solve for' setting and enter the known refraction angle.
How is ray bending direction determined?
Light bends toward the normal when entering an optically denser medium (n₂ > n₁) and away from the normal when entering a rarer medium (n₂ < n₁).
What units are used for input angles?
All angle inputs and calculation outputs are measured in degrees.