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Unformatted text preview: /λ was used. The position of the minimum waist of the transmitted beam is 7.50 cm to the right of the
2
lens (negative sign indicates the lens is to the left of the minimum waist). Using z0 = π w0 /λ again, we can calculate the new
minimum waist to be 0.0127 cm = 12.7 microns. 3.2 lens of ﬁnite thickness Lengths in centimeters, tobedetermined thickness d. M = 1 1−3/2
− (1)(−15) 0
3/2
1 1
0 d
1 1 3/2−1
− (3/2)(+5) 0
1
3/2 1 30 0 1 = 1 − d/15 −2/15 + d/450 30 − 4d/3 −3 + 2d/45 (22) We are intersted in the value of d that yields a z that is 10 percent diﬀerent than the z computed above. The introduction
of more material of index n will “pull” the waist closer to the lens, so we expect a meaningful solution only for 0.90 ∗ (−7.5)
(i.e. the ﬁrst solution for d when increasing d from zero).
The value of z is the real part of q :
(1 − d/15)(−iz0 ) + (30 − 4d/3)
z = Real[q ] = Real
(−2/15 + d/450)(−iz0 ) + (1 − d/45) The Matlab script below can be run (twice) to calculate the desired root. The answer is 1.94 cm.
clear all %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% calculate total matrix, in terms of variable thickness x
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
syms x
n = 3/2; 4 (23) a
b
c
d =
=
=
= [
[
[
[ 1
1
1
1 30
0
x
0 ;
;
;
; 0 1];
(n1)/(n*5) 1/n];
0 1];
(1n)/(15) n]; M = d*c*b*a; %%%%%%%%%%%%%%%%%%%%%%%%%%%%...
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This document was uploaded on 03/11/2014 for the course PHYS 408 at University of British Columbia.
 Fall '11
 KirkW.Madison
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