In [3]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
h = 6.626*10**-34; #Planck's constant(Js)
c = 3*10**8; #Speed of light in free space(m/s)
k = 1.38*10**-23; #Boltzmann constant(J/K)
T = 300; #Temperature at absolute scale(K)
lamda1 = 5500; #Wavelength of visible light(A)
lamda2 = 10**-2; #Wavelength of microwave(m)
#Calculation
lamda1 = lamda1*10**-10; #Wavelength of visible light(m)
rate_ratio = math.exp(h*c/(lamda1*k*T))-1; #Ratio of spontaneous emission to stimulated emission
rate_ratio1 = math.exp(h*c/(lamda2*k*T))-1; #Ratio of spontaneous emission to stimulated emission
rate_ratio1 = math.ceil(rate_ratio1*10**5)/10**5; #rounding off the value of rate_ratio1 to 5 decimals
#Result
print "The ratio of spontaneous emission to stimulated emission for visible region is",rate_ratio
print "The ratio of spontaneous emission to stimulated emission for microwave region is", rate_ratio1
```

In [4]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
e = 1.6*10**-19; #Energy equivalent of 1 eV(J/eV)
h = 6.626*10**-34; #Planck's constant(Js)
c = 3*10**8; #Speed of light in free space(m/s)
lamda = 690; #Wavelength of laser light(nm)
E_lower = 30.5; #Energy of lower state(eV)
#Calculation
lamda = lamda*10**-9; #Wavelength of laser light(m)
E = h*c/lamda; #Energy of the laser light(J)
E = E/e; #Energy of the laser light(eV)
E_ex = E_lower + E; #Energy of excited state of laser system(eV)
E_ex = math.ceil(E_ex*10**2)/10**2; #rounding off the value of E_ex to 2 decimals
#Result
print "The energy of excited state of laser system is",E_ex, "eV"
```

In [7]:

```
#importing modules
import math
from __future__ import division
import numpy as np
#Variable declaration
h = 6.626*10**-34; #Planck's constant(Js)
k = 1.38*10**-23; #Boltzmann constant(J/K)
#Calculation
#Stimulated Emission = Spontaneous Emission <=> exp(h*f/(k*T))-1 = 1 i.e.
#f/T = log(2)*k/h = A
A = np.log(2)*k/h; #Frequency per unit temperature(Hz/K)
A = A/10**10;
A = math.ceil(A*10**3)/10**3; #rounding off the value of A to 3 decimals
#Result
print "The stimulated emission equals spontaneous emission iff f/T =",A,"*10**10 Hz/k"
```

In [14]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
lamda = 500; #Wavelength of laser light(nm)
f = 15; #Focal length of the lens(cm)
d = 2; #Diameter of the aperture of source(cm)
P = 5; #Power of the laser(mW)
#Calculation
P = P*10**-3; #Power of the laser(W)
lamda = lamda*10**-9; #Wavelength of laser light(m)
d = d*10**-2; #Diameter of the aperture of source(m)
f = f*10**-2; #Focal length of the lens(m)
a = d/2; #Radius of the aperture of source(m)
A = math.pi*lamda**2*f**2/a**2; #Area of the spot at the focal plane, metre square
I = P/A; #Intensity at the focus(W/m**2)
I = I/10**7;
I = math.ceil(I*10**4)/10**4; #rounding off the value of I to 1 decimal
#Result
print "The area of the spot at the focal plane is",A, "m**2"
print "The intensity at the focus is",I,"*10**7 W/m**2"
```

In [17]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
h = 6.626*10**-34; #Planck's constant(Js)
c = 3*10**8; #Speed of light in free space(m/s)
lamda = 1064; #Wavelength of laser light(nm)
P = 0.8; #Average power output per laser pulse(W)
dt = 25; #Pulse width of laser(ms)
#Calculation
dt = dt*10**-3; #Pulse width of laser(s)
lamda = lamda*10**-9; #Wavelength of laser light(m)
E = P*dt; #Energy released per pulse(J)
E1 = E*10**3;
N = E/(h*c/lamda); #Number of photons in a pulse
#Result
print "The energy released per pulse is",E1,"*10**-3 J"
print "The number of photons in a pulse is", N
```

In [25]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
lamda = 693; #Wavelength of laser beam(nm)
D = 3; #Diameter of laser beam(mm)
d = 300; #Height of a satellite above the surface of earth(km)
#Calculation
D = D*10**-3; #Diameter of laser beam(m)
lamda = lamda*10**-9; #Wavelength of laser beam(m)
d = d*10**3; #Height of a satellite above the surface of earth(m)
d_theta = 1.22*lamda/D; #Angular spread of laser beam(rad)
dtheta = d_theta*10**4;
dtheta = math.ceil(dtheta*10**2)/10**2; #rounding off the value of dtheta to 2 decimals
a = d_theta*d; #Diameter of the beam on the satellite(m)
a = math.ceil(a*10)/10; #rounding off the value of a to 1 decimal
#Result
print "The height of a satellite above the surface of earth is",dtheta,"*10**-4 rad"
print "The diameter of the beam on the satellite is",a, "m"
```

In [ ]:

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