๐ Snellโs Law (Refraction) Calculator
Enter the incident angle and the refractive indices of two media (n1, n2) to calculate the refraction angle using Snellโs law (n1รsinฮธ1=n2รsinฮธ2). If total internal reflection occurs, this is indicated along with the critical angle.
How to use
- Enter the refractive index of the incident medium (n1), e.g. air = 1.0.
- Enter the incident angle (degrees).
- Enter the refractive index of the second medium (n2), e.g. water = 1.33, glass = 1.5.
- The refraction angle is shown, or if total internal reflection occurs, that fact and the critical angle are shown instead.
How the calculation works
This tool calculates how much light bends (refracts) when it crosses the boundary between two materials, such as from air into water or glass. Snellโs law: n1 ร sin ฮธ1 = n2 ร sin ฮธ2 n1 and n2 are the refractive indices of the materials before and after the boundary, ฮธ1 is the angle of incidence and ฮธ2 the angle of refraction. Angles are measured from the normal, the line perpendicular to the surface. Going into a material with a higher index, light bends toward the normal. Going into a lower index, light cannot get out once the angle of incidence exceeds the critical angle, and it is all reflected (total internal reflection). The critical angle is given by sin ฮธc = n2 รท n1.
Worked example
From air (n1 = 1.0) into glass (n2 = 1.5) at 30ยฐ sin ฮธ2 = 1.0 ร sin 30ยฐ รท 1.5 = 0.333 โ refraction angle about 19.47ยฐ From water (1.33) into air (1.0) at 40ยฐ Refraction angle about 58.75ยฐ Critical angle from water into air: about 48.75ยฐ Critical angle from glass (1.5) into air: about 41.81ยฐ
Things to be aware of
- The refractive index varies slightly with colour (wavelength). That is why a prism splits white light into a rainbow.
- Refraction is why objects under water look shallower than they are and why a straw looks bent in a glass.
- Optical fibres carry light over long distances by bouncing it along the glass with total internal reflection.
FAQ
What is total internal reflection?
When light travels from a denser medium (higher refractive index) into a less dense one, and the incident angle exceeds the critical angle, all the light is reflected instead of refracting. This is the principle behind optical fibers.
How is the critical angle calculated?
Itโs calculated as sin(critical angle) = n2/n1, and only exists when n1 is greater than n2 (going from denser to less dense).
What values should I use for refractive index?
Vacuum and air are approximately 1.0, water is approximately 1.33, common glass is approximately 1.5, and diamond is approximately 2.42 โ use the value for your medium.