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Material Type: Assignment; Class: 1051 - Physical Optics; Subject: Imaging Science; University: Rochester Institute of Technology; Term: Spring 2010;
Typology: Assignments
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n [] = A 0 +
where A 0 and B 0 are empirically determined constants and 0 is the wavelength of light in a vacuum. If A 0 = 1: 40 , B 0 = 2: 5 104 ( nm)^2 , determine the phase and group velocities at 0 = 500 nm.
n [ = 500 nm] = 1 :40 +^2 :^5 ^10
(^4) ( nm)^2 (500 nm)^2
v [ = 500 nm] =
n
jk 0 j
c n
(^8) m s 1 1 : 5
= v = 2: 0 10 8 ms
The ìgroup velocityî may also be called the ìmodulation velocityî v (^) mod , which is the speed of the low-frequency modulation. We need to Önd an expression for the modulation velocity in terms of the numbers we know:
vmod = d! dk (^) =500 nm v =
k =)^!^ =^ k^ ^ v^ =^ k^ ^
c n =) d! dk
d dk
k c n
c n
dk dk
k n
dc dk
n
vmod = d! dk
c n
k n 0 + kc