In 1836, A. Cauchy wrote a purely empirical relationship (i. e. , there is no th
ID: 1918546 • Letter: I
Question
In 1836, A. Cauchy wrote a purely empirical relationship (i. e. , there is no theoretical justification other than that it works) between the refractive index of a substance and wavelength. It is valid in the visible range for many different transparent substances. The Cauchy equation is: n = A + Blambda-2 where A and B are the Cauchy coefficients, and are different for different materials. Wikipedia will tell you the coefficients of the Cauchy equation for six different types of glass. For water, you can use A = 1. 31885 and B = 0. 005174. In general, does blue light in glass travel faster or slower than red light? Justify your answer. Which of the glass materials has about the same dispersion as water? Justify your answer.Explanation / Answer
n = A + B/2
From Wikipedia:
(a) Blue light has a shorter wavelength and higher frequency than red light. So, the index of refraction will be higher for blue light than red light since it depends on the reciprocal square of the wavelength. The speed of light is c/n, so red light will travel faster since it will have the lower index of refraction.
(b) For water, A = 1.31885 and B = 0.005174. Dispersion relates to the splitting of white light into its constituent colors, as in a prism. So, we are looking for the material with the B term closest to that of water. That would be Barium crown glass BaK4.
Material A B (m2) Fused silica 1.4580 | 0.00354 Borosilicate glass BK7 1.5046 | 0.00420 Hard crown glass K5 1.5220 | 0.00459 Barium crown glass BaK4 1.5690 | 0.00531 Barium flint glass BaF10 1.6700 | 0.00743 Dense flint glass SF10 1.7280 | 0.01342