Calculate the angle of refraction from refractive indices and incidence angle using Snell's law, with total-internal-reflection detection.
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Snell's law calculator Use Snell's law to estimate the angle of refraction when light crosses from one medium into another. This page also flags total internal reflection when the refracted ray no longer exists.
Formula reference
n₁ sin θ₁ = n₂ sin θ₂
θ₂ = arcsin((n₁ × sin θ₁) ÷ n₂)
The shortcut works best for a sharp interface, a known pair of refractive indices, and angles measured from the normal.
Refraction result
19.47°
Angle of refraction for light moving from refractive index 1 into 1.5 at an incidence angle of 30°.
Angle of refraction
19.47°
Incidence angle
30°
Medium 1 index
1
Medium 2 index
1.5
How to read the result If the second medium has a higher refractive index, the refracted ray bends toward the normal and the angle becomes smaller. If the second medium has a lower refractive index, the ray bends away from the normal until the total-internal-reflection threshold is reached.
Snell's law calculator guide: find the angle of refraction or spot total internal
A Snell's law calculator helps you estimate the angle of refraction when light passes from one medium into another. By combining the refractive indices of the two media with the angle of incidence, the page solves the refraction angle directly from n₁ sin θ₁ = n₂ sin θ₂ and also flags when total internal reflection occurs instead of refraction.
What Snell's law describes
Snell's law describes how a ray bends at the boundary between two media with different refractive indices. If light enters a slower medium with a higher refractive index, the refracted ray bends toward the normal. If it enters a faster medium with a lower refractive index, the ray bends away from the normal.
The law is one of the standard tools of geometric optics because it links the incident angle, the refractive indices, and the refracted angle in a single relationship.
The Snell's law formula
The standard form is n₁ sin θ₁ = n₂ sin θ₂. Here n₁ and n₂ are the refractive indices of the first and second media, θ₁ is the angle of incidence, and θ₂ is the angle of refraction. All angles are measured from the normal rather than from the surface.
To solve for the refracted angle, rearrange the equation to θ₂ = arcsin((n₁ × sin θ₁) ÷ n₂). If the term inside arcsin is greater than 1 in magnitude, no real refracted angle exists and the boundary is in total internal reflection.
n₁ sin θ₁ = n₂ sin θ₂
The standard refraction relationship for a sharp boundary between two media.
θ₂ = arcsin((n₁ × sin θ₁) ÷ n₂)
The rearranged form used by this calculator to solve the angle of refraction.
Worked example: air into glass
Suppose light travels from air with refractive index 1.00 into glass with refractive index 1.50 at an incidence angle of 30°. The sine term becomes 1.00 × sin 30° ÷ 1.50 = 0.3333, so the refracted angle is about 19.47°.
That smaller angle makes physical sense because light is entering the higher-index medium and bending toward the normal. The calculator shows the same relationship directly in the result card.
When total internal reflection happens
Total internal reflection happens when light tries to move from a higher-index medium into a lower-index medium at an angle above the critical angle. In that situation, the sine term needed for the refracted angle becomes greater than 1, so there is no real refracted ray.
The calculator does not force a fake number in that case. Instead, it flags total internal reflection so you know the physical outcome is reflection at the boundary rather than a transmitted refracted ray.
Further reading
Wavelength Calculator — Use the Wavelength Calculator when you need the wave-equation relationship between wavelength, frequency, and speed.
Frequency Wavelength Converter — Use the Frequency Wavelength Converter when the optics problem needs broader frequency and wavelength conversions.
Wavelength Helper — Use the Wavelength Helper when you want additional wave-speed and medium reference examples.
Limits of this Snell's law calculator
This page assumes a sharp interface and uses scalar refractive-index values. It does not model polarization effects, absorption, anisotropic media, surface roughness, or full wave-optics behavior.
Use it as a geometric-optics tool for standard refraction problems. If the setup involves graded-index materials, complex media, or interference effects, a more detailed optics model is needed.
Frequently asked questions
How do you calculate the angle of refraction?
Use Snell's law: n₁ sin θ₁ = n₂ sin θ₂. Rearranging gives θ₂ = arcsin((n₁ × sin θ₁) ÷ n₂).
What is Snell's law?
Snell's law describes how light bends when it crosses the boundary between two media with different refractive indices.
Why are the angles measured from the normal?
That is the standard convention in optics. Measuring from the normal keeps the geometry consistent with the Snell's law formula.
What happens when the refracted-angle calculation fails?
If the sine term would be greater than 1 in magnitude, no real refracted angle exists and the boundary is in total internal reflection.
What is total internal reflection?
It is the condition where light stays in the first medium and reflects back instead of refracting into the second medium.
Can Snell's law be used for air to glass?
Yes. That is one of the most common textbook cases. Light entering glass from air bends toward the normal because glass has the higher refractive index.
Can Snell's law be used for glass to air?
Yes, but if the incidence angle is too large the result may switch to total internal reflection rather than refraction.
Does this calculator find the critical angle?
No. It focuses on the refracted-angle form of Snell's law and flags total internal reflection when the requested setup passes the limit.
Does Snell's law work for all optics problems?
No. It works well for standard geometric-optics boundaries, but it does not replace full wave-optics or anisotropic-medium analysis.
What is the difference between refractive index and angle of refraction?
Refractive index is a material property that describes how strongly light slows in a medium. The angle of refraction is the direction the ray takes after crossing the boundary.
