11: Lasers

Example number 11.1, Page number 11.55

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=20*10**-3;      #power(watt)
r=1.3/2;     #radius(mm)

#Calculation
r=r*10**-3;    #radius(m)
I=P/(math.pi*r**2);     #intensity of laser beam(watt/m**2)

#Result
print "intensity of laser beam is",round(I/10**4,1),"*10**4 watt/m**2"
print "answer given in the book is wrong"

intensity of laser beam is 1.5 *10**4 watt/m**2
answer given in the book is wrong

Example number 11.2, Page number 11.56

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

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
L=0.6;      #distance(m)

#Calculation
delta_v=c/(2*L);    #mode seperation in frequency(Hz)

#Result
print "mode seperation in frequency is",delta_v/10**8,"*10**8 Hz"

mode seperation in frequency is 2.5 *10**8 Hz

Example number 11.3, Page number 11.56

In [19]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
delta_t=0.05*10**-9;    #time(s)
lamda=623.8*10**-9;    #wavelength(m)

#Calculation
cl=c*delta_t;    #coherence length(m)
delta_v=1/delta_t;    #band width(Hz)
delta_lamda=lamda**2*delta_v/c;    #line width(m)

#Result
print "coherence length is",cl*10**2,"*10**-2 m"
print "band width is",delta_v/10**10,"*10**10 Hz"
print "line width is",round(delta_lamda*10**9,3),"nm"

coherence length is 1.5 *10**-2 m
band width is 2.0 *10**10 Hz
line width is 0.026 nm

Example number 11.4, Page number 11.56

In [21]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
h=6.63*10**-34;    #plank's constant(Js)
lamda=632.8*10**-9;    #wavelength(m)
e=1.6*10**-19;     #charge(coulomb)

#Calculation
E=c*h/(lamda*e);    #energy difference(eV)

#Result
print "energy difference is",round(E,2),"eV"

energy difference is 1.96 eV

Example number 11.5, Page number 11.57

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
h=6.63*10**-34;    #plank's constant(Js)
lamda=6928*10**-10;    #wavelength(m)
Kb=1.38*10**-23;    #boltzmann constant(J/K)
T=291;    #temperature(K)

#Calculation
delta_E=c*h/lamda;
N=math.exp(-delta_E/(Kb*T));    #ratio of population

#Result
print "ratio of population is",round(N*10**32,2),"*10**-32"
print "answer given in the book is wrong"

ratio of population is 8.95 *10**-32
answer given in the book is wrong

Example number 11.6, Page number 11.57

In [26]:
#importing modules
import math
from __future__ import division

#Variable declaration
Kb=1.38*10**-23;    #boltzmann constant(J/K)
T=330;    #temperature(K)
delta_E=3.147*10**-19;       #energy(J)
c=3*10**8;    #velocity of light(m/sec)
h=6.63*10**-34;    #plank's constant(Js)

#Calculation
lamda=c*h/delta_E;    #wavelength(m)

#Result
print "wavelength is",int(lamda*10**9),"*10**-9 m"

wavelength is 632 *10**-9 m

Example number 11.7, Page number 11.58

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
r1=2*10**-3;    #radius(m)
r2=3*10**-3;     #radius(m)
d1=2;     #distance(m)
d2=4;     #distance(m)

#Calculation
delta_theta=(r2-r1)/(d2-d1);     #laser beam divergence(radian)

#Result
print "laser beam divergence is",delta_theta*10**3,"*10**-3 radian"

laser beam divergence is 0.5 *10**-3 radian

Example number 11.8, Page number 11.58

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
h=6.63*10**-34;    #plank's constant(Js)
lamda=6943*10**-10;    #wavelength(m)
Kb=1.38*10**-23;    #boltzmann constant(J/K)
T=300;    #temperature(K)

#Calculation
new=c/lamda;
N=math.exp(h*new/(Kb*T));    #ratio of population

#Result
print "ratio of population is",round(N*10**-30,3),"*10**30"
print "answer given in the book is wrong"

ratio of population is 1.127 *10**30
answer given in the book is wrong

Example number 11.9, Page number 11.58

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
h=6.63*10**-34;    #plank's constant(Js)
Eg=1.44*1.6*10**-19;    #band gap(J)

#Calculation
lamda=c*h/Eg;     #wavelength(m)

#Result
print "wavelength is",round(lamda*10**10,1),"angstrom"
print "answer given in the book is wrong"

wavelength is 8632.8 angstrom
answer given in the book is wrong

Example number 11.10, Page number 11.59

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=1.55;     #wavelength(micro m)

#Calculation
Eg=1.24/lamda;      #energy gap(eV)

#Result
print "energy gap is",Eg,"eV"

energy gap is 0.8 eV

Example number 11.11, Page number 11.59

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
c=3*10**8;    #velocity of light(m/sec)
tow=4*10**-5;    #time(sec)
lamda=740*10**-9;     #wavelength(m)

#Calculation
L=tow*c;     #coherence length(m)
delta_lamda=lamda**2/L;     #spectral half width(m)
Q=lamda/delta_lamda;     #purity factor

#Result
print "coherence length is",int(L/10**3),"*10**3 m"
print "spectral half width is",round(delta_lamda*10**17,2),"*10**-17 m"
print "purity factor is",round(Q/10**10,1),"*10**10"

coherence length is 12 *10**3 m
spectral half width is 4.56 *10**-17 m
purity factor is 1.6 *10**10

Example number 11.12, Page number 11.59

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
new=5.9*10**14;    #frequency(Hz)
h=6.63*10**-34;    #plank's constant(Js)
Kb=1.38*10**-23;    #boltzmann constant(J/K)
T=2500;    #temperature(K)

#Calculation
R=math.exp(h*new/(Kb*T))-1;     #ratio of emissions

#Result
print "ratio of emissions is",round(R/10**4,1),"*10**4"
print "answer given in the book is wrong"

ratio of emissions is 8.4 *10**4
answer given in the book is wrong

Example number 11.13, Page number 11.60

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=1.06*10**-6;      #wavelength(m)
d=2.54*10**-2;     #distance(m)

#Calculation
theta=2.44*lamda/d;      #beam divergence(radian)

#Result
print "beam divergence is",round(theta*10**4,2),"*10**-4 radian"

beam divergence is 1.02 *10**-4 radian

Example number 11.14, Page number 11.60

In [23]:
#importing modules
import math
from __future__ import division

#Variable declaration
P=2.3*10**-3;    #power(W)
c=3*10**8;    #velocity of light(m/sec)
h=6.63*10**-34;    #plank's constant(Js)
lamda=6328*10**-10;    #wavelength(m)

#Calculation
n=P*lamda*60/(c*h);      #number of photons/min

#Result
print "number of photons/minute is",round(n/10**17,2),"*10**17"

number of photons/minute is 4.39 *10**17