How to use the snell law calculator
- Enter the refractive index of the first material, where the light starts. Air is close to 1 and water is about 1.33.
- Enter the index of the second material, where the light goes.
- Enter the angle of incidence in degrees, measured from the normal, the line at right angles to the surface.
- Read the refracted angle, the bend, and the critical angle when light goes toward a less dense material.
Formula
n1 x sin(angle 1) = n2 x sin(angle 2)
angle 2 = arcsin(n1 x sin(angle 1) / n2)
critical angle = arcsin(n2 / n1), when n1 is larger than n2
When the right side of the arcsine would be more than 1, no refracted ray exists and all of the light reflects. The reflected ray leaves at the same angle as the incoming ray.
Light from air into water at 30 degrees
With n1 = 1, n2 = 1.33 and an incident angle of 30 degrees, sin(angle 2) = 1 x 0.5 / 1.33 = 0.3759, so angle 2 = arcsin(0.3759) = 22.08 degrees. The light bends toward the normal.
Going the other way, from glass (1.5) into air (1) at 30 degrees gives sin(angle 2) = 1.5 x 0.5 = 0.75, and angle 2 = 48.59 degrees. The critical angle for glass to air is arcsin(1 / 1.5) = 41.81 degrees, so a ray at 45 degrees from inside glass is totally reflected.
Bending toward and away from the normal
Light slows down in a material with a higher refractive index. When it enters a slower material, it bends toward the normal. When it enters a faster one, it bends away. The page reports the speed in the second material compared with the first, which is the ratio n1 divided by n2.
At straight-on incidence, 0 degrees, light does not bend at all. When both indexes match, there is no boundary effect, so the angle stays the same.
Where the numbers come from
Refractive index depends on the color of the light and on temperature, so published values are quoted for a stated wavelength. The values in the help text are rounded examples. For other physics problems, see the Pendulum Period Calculator and the Kinematics Calculator, or use the Scientific Calculator to check the sines yourself.
Assumptions and limits
- The surface is flat and both materials are uniform.
- The refractive index is the same for all colors of light, which is an approximation.
- Reflection strength and polarization are not modeled.
- The angle is measured from the normal, not from the surface.
Frequently asked questions
What is Snell's law?
It says that the product of the refractive index and the sine of the angle is the same on both sides of a boundary between two materials. It lets you find how far light bends.
How do I find the critical angle?
Take the arcsine of the second index divided by the first. For glass at 1.5 into air at 1 it is arcsin(1 / 1.5), which is 41.81 degrees. It only exists when light goes to a lower index.
What is total internal reflection?
When light inside a denser material hits the surface at more than the critical angle, none of it passes out and all of it reflects. The page says so instead of giving a refracted angle.
Why is the angle measured from the normal?
The normal is the line perpendicular to the surface, and the law is written in terms of angles to that line. An angle measured from the surface itself is 90 degrees minus the angle to the normal.