How to Calculate the Angle of a Refraction

When a ray of light (an incident ray) passes through the interface of two media (e.g. air and water) it changes its speed and direction. As a result the refracted ray has a different angle than the incident ray. Snell's law establishes the relationship between magnitudes of incident and refracted angles via refractive indexes of two media. Sin(incident angle)/ Sin(refracted angle)=refractive index (second medium)/ refractive index (first medium). A refractive index is usually abbreviated as "n."

Things You'll Need

• Calculator

Instructions

The Steps

1. Obtain refractive indexes of the two media using the table of refractive indexes (see resources). In our example, n(Air) is 1.00 and n(Water) is 1.33.

2. Calculate sine of the incident angle. In our example, Sin(incident angle)=sin(30 degrees)=0.5.

3. Calculate sine of the refracted angle using the formula. Sin(refracted angle)=Sin(incident angle) x refractive index (first medium)/ refractive index (second medium). In our example, Sin(refracted angle)= Sin(incident angle) x n(Air)/ n(Water)=0.5 x 1.00/1.33= 0.3759.

4. Calculate the angle of refraction using the arcsine operation. Refracted angle=arcsin(sin(reflected angle)). In our example, refracted angle is arcsin(0.3759)=22.08 degrees.

References

• "Optics", E. Hecht, Aug. 12, 2001.

Resources

• Read this Article in Spanish
• Table of refractive indexes