Question

6. The dispersion curve of dense flint glass can be represented approximately by Cauchy's empirical equation, n = A + B/22, where 2 is the wavelength in free space. Find the phase velocity (W/k) and group velocity (w/ak) for light with 2 = 550 nm, in a particular glass for which A = 1.7280 and B = 0.01342 uma. 720

Answer 1

Given Dala. So1: The Osspersien' leurre of dense ight lint glais can be represented appmimately by cauchy's empherscal Eajualiên : n=A+B/j" wohere a is the oave Length in Free Spale. we have to Find the Free Space velocity (0/K) For phase and group Velo city (aw/ak) For Ught wath a=5500m. particular glass For wnich A= 11728o and B=0.01342Mm". The phase delo city of a uave is the rate at wwhich the phase Of the Wave propogates in space. Tuis is the velocity at which ene freajueny Component of the woave phase of amy the travels. The Group velocêty of a uwave is the velocity wofth which the overall envelop shape of the naves amplitude - Kmown as the modulalion or) envelope of the wwave propogates though space ne AtB/xr A=11280 5500 A° A= 550 nm= B = 1342 XL06 A° 1:34 X105 n=1.7280 + (5500)" 1.7722 phase specd p n= 3x105 1.7722 Mp = 1.69X10 mlsee Epaup Speed z phare Speed = l.69 X1of mls