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Angle of Refraction Calculator

Our angle of refraction calculator can help you find the bending path of a wave from Snell's law.

Clear
Angle of refraction28.8392°bent TOWARDS the normal, because the light slowed down entering a denser medium
Deviation from the original path11.1608°
Refractive indices1.0003 → 1.333Air into Water
Angle of incidence40°measured from the normal to the surface
Speed of light in air299.7046 Mm/s99.971% of c
Speed of light in water224.9006 Mm/s75.019% of c — refraction happens because the wave changes speed, and the frequency does not change
No critical angle this waygoing into a denser mediumtotal internal reflection only happens travelling from a higher index to a lower one
Brewster's angle53.1152°at this incidence the reflected light is completely polarised — which is how polarising sunglasses cut glare off water
Wavelength ratio0.750407the wavelength shortens in the denser medium while the frequency — and so the colour — stays the same

The formula

n₁ sin θ₁ = n₂ sin θ₂; critical angle = arcsin(n₂ ÷ n₁)

Frequency stays, wavelength changes

Light slows when it enters a denser medium, and Snell's law says the sines of the angles are in inverse proportion to the speeds. Entering a denser medium bends the ray towards the normal; leaving one bends it away.

What does not change is the frequency. The source is still oscillating at the same rate, so the slower speed shows up entirely as a shorter wavelength. This is why light does not change colour underwater even though its wavelength there is a quarter shorter.

Going from a dense medium to a thinner one has a limit. Past the critical angle there is no solution to Snell's law at all and the light reflects entirely — total internal reflection. That is what confines light in an optical fibre, and diamond's critical angle of about 24° is why so much light entering a cut stone bounces around inside before escaping.

At Brewster's angle the reflected light is completely polarised in one direction, which is what polarising sunglasses exploit to remove glare from water and roads. Note that all these indices are quoted at 589 nm; index varies with wavelength, and that dispersion is what makes a prism split white light into colours.