Snell's Law Calculator
Find the refraction angle as light crosses a boundary.
Results update as you type.
How it works
When light crosses from one transparent material into another, it bends, and Snell's law predicts exactly how much. This calculator finds the angle of refraction from the refractive indices of the two media and the angle at which light strikes the boundary. You enter the index of the first medium, the incidence angle measured from the perpendicular, and the index of the second medium, and it returns the refraction angle. Light slows down in denser media, which have higher refractive indices, and bends toward the perpendicular when entering a denser medium and away from it when entering a less dense one. This bending is why a straw looks broken in a glass of water, why lenses can focus light, and why prisms split white light into colours. The calculator also detects total internal reflection, which happens when light travels from a denser to a less dense medium at a steep enough angle that it cannot escape and reflects entirely back; this effect is the basis of fibre-optic cables that carry the internet. Physics and optics students use Snell's law constantly, as do lens and camera designers. Enter the two indices and the incidence angle to find the refraction angle.
n₁ · sin θ₁ = n₂ · sin θ₂
Snell's law relates the angles of incidence and refraction when light passes between two media to their refractive indices: the product of the first index and the sine of the incidence angle equals the product of the second index and the sine of the refraction angle. Solving for the refraction angle takes the inverse sine of the first index times the sine of incidence, divided by the second index.
Source:Optics (Snell's law of refraction)
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Worked example
How to use this calculator
- 1
Enter your values
Enter index of medium 1 (n₁), angle of incidence (θ₁) and index of medium 2 (n₂).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Angle of refraction (θ₂) updates instantly as you type — no button to press.
Frequently asked questions
What is Snell's law?
Snell's law describes how light bends, or refracts, when it passes from one medium into another. It states that the refractive index of the first medium times the sine of the incidence angle equals the refractive index of the second medium times the sine of the refraction angle. It lets you predict the exact angle light takes after crossing a boundary.
What is the refractive index?
The refractive index of a material measures how much it slows down light compared with a vacuum. A vacuum has an index of exactly 1, air is very close to 1, water is about 1.33, and glass is around 1.5. A higher index means light travels more slowly and bends more sharply when entering or leaving that medium.
Which way does light bend?
Light bends toward the perpendicular, or normal, when it enters a denser medium with a higher refractive index, and away from the normal when it enters a less dense medium. This is why light entering water from air bends toward the normal. The calculator computes the exact refraction angle based on the two indices you provide.
What is total internal reflection?
Total internal reflection occurs when light travelling from a denser medium to a less dense one hits the boundary at an angle beyond the critical angle. Instead of refracting through, all the light reflects back into the denser medium. This calculator flags when it happens. The effect is what makes fibre-optic cables, prisms in binoculars, and sparkling diamonds work.
Why does a straw look bent in water?
Light from the submerged part of the straw refracts as it leaves the water and enters the air, bending at the surface according to Snell's law. Your eyes trace the light back in a straight line, so the underwater part appears shifted, making the straw look broken or bent at the waterline. It is a everyday demonstration of refraction.