Lasers

Example number 2.1, Page number 52

In [1]:
#To calculate the relative population 

#importing modules
import math

#Variable declaration
lamda = 590;        #wavelength(nm)
h = 6.625*10**-34;       #planck's constant
c = 3*10**8;            #velocity of light(m/s)
k = 1.38*10**-23;       #boltzmann's constant
T = 523;                #temperature(Kelvin)

#Calculation
lamda = lamda*10**-9;      #wavelength(m)      
#n1byn2 = math.exp(-(E2-E1)/(k*T))
#but E2-E1 = h*new and new = c/lamda
#therefore n1byn2 = math.exp(-h*c/(lamda*k*T))
n1byn2 = math.exp(-h*c/(lamda*k*T));

#Result
print "relative population of Na atoms is",n1byn2

relative population of Na atoms is 5.36748316686e-21

Example number 2.2, Page number 53

In [4]:
#To calculate the ratio of stimulated to spontaneous emission 

#importing modules
import math

#Variable declaration
lamda = 590;        #wavelength(nm)
h = 6.625*10**-34;       #planck's constant
c = 3*10**8;            #velocity of light(m/s)
k = 1.38*10**-23;       #boltzmann's constant
T = 523;                #temperature(Kelvin)

#Calculation
lamda = lamda*10**-9;      #wavelength(m)      
#n21dashbyn21 = 1/(math.exp(h*new/(k*T))-1)
#but new = c/lamda
#therefore n21dashbyn21 = 1/(math.exp(h*c/(lamda*k*T))-1)
A = math.exp(h*c/(lamda*k*T))-1;
n21dashbyn21 = 1/A;    

#Result
print "ratio of stimulated to spontaneous emission is",n21dashbyn21
print "answer given in the book is wrong"

ratio of stimulated to spontaneous emission is 5.36748316686e-21
answer given in the book is wrong

Example number 2.3, Page number 53

In [5]:
#To calculate the number of photons emitted 

#importing modules
import math

#Variable declaration
lamda = 632.8;        #wavelength of laser(nm)
h = 6.625*10**-34;       #planck's constant
c = 3*10**8;            #velocity of light(m/s)
p = 3.147;              #output power(mW)

#Calculation
p = p*10**-3;          #output power(W)
lamda = lamda*10**-9;      #wavelength(m)      
new = c/lamda;             #frequency(Hz)
E = h*new;                 #energy of each photon(J)
Em = p*60;                 #energy emitted per minute(J/min)
N = Em/E;                  #number of photons emitted per second

#Result
print "number of photons emitted per second is",N

number of photons emitted per second is 6.01183879245e+17
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