Using the small-angle approximation to measure the index of refraction of water

We describe a simple experiment that allows us to measure the index of refraction of water by making a series of length measurements. The ratio of two length measurements gives the ratio of the tangent of the angle of incidence to that of the angle of refraction. As the angle of incidence decreases, so do the values of the tangents, and their values approach those of the sines. The limiting value of the ratio is equal to the index of refraction. Our results for water were an index value of 1.33 ± 0.01, an error of less than 1 percent. The method uses length measurements only and obviates all angle measurements.