15: Lasers

Example number 15.1, Page number 283

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
k=1.38*10**-23;   #boltzmann constant(J/K)
T=1000;    #temperature(K)
new1=7.5*10**14;  
new2=4.3*10**14;
h=6.626*10**-34;    #planck's constant(Js)

#Calculation
kT=k*T;
#optical region extends from 4000 to 7000 angstrom
hnew=h*(new1-new2);  

#Result
print "value of kT is",kT,"J"
print "value of hnew is",hnew,"J"
print "hnew>kT.therefore spontaneous transitions are dominant ones in optical region"

value of kT is 1.38e-20 J
value of hnew is 2.12032e-19 J
hnew>kT.therefore spontaneous transitions are dominant ones in optical region

Example number 15.2, Page number 298

In [6]:
#importing modules
import math
from __future__ import division

#Variable declaration
h=6.626*10**-34;    #planck's constant(Js)
c=3*10**8;    #velocity of light(m/sec)
P=0.6;   #power(watt)
T=30*10**-3;    #time(s)
lamda=640*10**-9;   #wavelength(m)

#Calculation
E=P*T;    #energy deposited(J)
n=E*lamda/(h*c);   #number of photons in each pulse

#Result
print "energy deposited is",E,"J"
print "number of photons in each pulse is",round(n/10**16,1),"*10**16"

energy deposited is 0.018 J
number of photons in each pulse is 5.8 *10**16

Example number 15.3, Page number 298

In [11]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5000*10**-10;   #wavelength(m)
f=0.2;   #focal length(m)
a=0.009;   #radius of aperture(m)
P=2.5*10**-3;   #power(W)

#Calculation
A=math.pi*lamda**2*f**2/a**2;    #area of spot at focal plane(m**2)
I=P/A;   #intensity at focus(W/m**2)

#Result
print "area of spot at focal plane is",round(A*10**10,2),"*10**-10 m**2"
print "intensity at focus is",round(I/10**6,3),"*10**6 W/m**2"

area of spot at focal plane is 3.88 *10**-10 m**2
intensity at focus is 6.446 *10**6 W/m**2

Example number 15.4, Page number 298

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=693*10**-9;   #wavelength(m)
D=3*10**-3;    #diameter of mirror(m)
d=300*10**3;   #distance from earth(m)

#Calculation
delta_theta=1.22*lamda/D;    #angular spread(rad)
a=delta_theta*d;    #diameter of beam on satellite(m)

#Result
print "angular spread is",round(delta_theta*10**4,2),"*10**-4 rad"
print "diameter of beam on satellite is",round(a,2),"m"

angular spread is 2.82 *10**-4 rad
diameter of beam on satellite is 84.55 m