Refraction and Snell's Law Calculator
Enter the refractive index of each material and the angle of the incoming ray. You get the refracted angle, or total internal reflection, and the critical angle.
The normal is the line at right angles to the surface. Refractive indexes are typical values for yellow light.
Worked examples
Into water
Air to water at 30 degrees
22.0 degrees
sin(angle) = 1.0003 x 0.5 / 1.333.
Critical angle
Glass (1.52) to air
41.1 degrees
arcsin(1 / 1.52).
About Refraction and Snell's Law Calculator
When light passes from one transparent material into another, it changes speed and its path bends. Snell's law says the refractive index of the first material times the sine of the angle in it equals the index of the second material times the sine of the angle in that. Entering a denser material, such as air into water, bends the ray towards the normal, the line at right angles to the surface. Leaving it bends the ray away.
If light tries to leave a denser material at a steep angle, it cannot get out and is reflected back inside. This is total internal reflection, and it happens above the critical angle, which is the arcsine of the ratio of the indexes. It is how optical fibres, binoculars and the sparkle of a diamond work. This page gives the refracted angle or tells you total internal reflection occurs, together with the critical angle and the speed of light in each material.
How to use Refraction and Snell's Law Calculator
- Enter the refractive index of each material, or pick one from the menus.
- Enter the angle of the incoming ray measured from the normal.
- Read the angle of refraction, or the message about total internal reflection.
- Check the critical angle and the speed of light in each material.
Common uses
- Optics homework on refraction and total internal reflection
- Understanding why a straw looks bent in water
- Designing a simple prism or light pipe
- Working out the critical angle of a glass or acrylic block
Frequently asked questions
What is Snell's law?
n1 x sin(angle 1) = n2 x sin(angle 2), where n is the refractive index of each material and the angles are measured from the normal.
What is the critical angle?
It is the angle of incidence inside a denser material above which light is totally reflected. It equals arcsin(n2 / n1). For glass to air it is about 41 degrees.
What is refractive index?
It is the speed of light in a vacuum divided by the speed in the material. Water is about 1.33, glass about 1.5 and diamond 2.42.
Why does the same material bend colours differently?
The index depends slightly on the wavelength, so blue light bends more than red. This is dispersion, and it makes a prism split white light.