A sample of heavy flint glass has measured refractive indices at 486 nm and at 656 nm

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Wave propagation and light in media · Wave propagation and light in media

Optics and Photonics, Ch Light as an electromagnetic wave in matter

Problem

A sample of heavy flint glass has measured refractive indices

n = 1.8419

at 486 nm and

n = 1.8161

at 656 nm, and

n = 1.8236

at 589 nm. Its dispersion also follows the Cauchy fit

n = A + B/\lambda^2

with

A = 1.7847

and

B = 13500\ \text{nm}^2

(

\lambda

in nanometres). ((a)) Using only the two measured points at 486 nm and 656 nm, form the chord slope

\Delta n/\Delta\lambda

(the two-point method of Chapter 4) and use it to estimate the group index

n_g \approx n - \lambda(\Delta n/\Delta\lambda)

at 589 nm. ((b)) Using the Cauchy fit directly, find the exact group index

n_g = n + 2B/\lambda^2

at 589 nm. ((c)) Compute the group velocity

v_g = c/n_g

from each method and state which one is more reliable and why.