14: Optics

Example number 14.1, Page number 14.41

In [39]:
#importing modules
import math
from __future__ import division

#Variable declaration
I1=10;     #intensity(w/m**2)
I2=25;     #intensity(w/m**2)

#Calculation
a1bya2=math.sqrt(I1/I2);    
I=((1+a1bya2)**2)/((a1bya2-1)**2);    #ratio of maximum intensity to minimum intensity

#Result
print "ratio of maximum intensity to minimum intensity is",round(I,3)
print "answer varies due to rounding off errors"

ratio of maximum intensity to minimum intensity is 19.727
answer varies due to rounding off errors

Example number 14.2, Page number 14.42

In [40]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5460*10**-10;    #wavelength(m)
d=1*10**-4;     #seperation(m)
D=2;     #distance(m)
n=10;    #position

#Calculation
Xmax10=n*lamda*D/d;
tan_phi=Xmax10/D;     
phi_max10=math.atan(tan_phi);
phi_max10=phi_max10*180/math.pi;     #angular position of 10th maximum(degrees)
phim=60*(phi_max10-int(phi_max10));
phis=60*(phim-int(phim));
xmin1=lamda*D/(2*d);       
tan_phi1=xmin1/D;
phi_min1=math.atan(tan_phi1);
phi_min1=phi_min1*180/math.pi;     #angular position of 1st minimum(degrees)
phi_m=60*(phi_min1-int(phi_min1));
phi_s=60*(phi_m-int(phi_m));

#Result
print "angular position of 10th maximum is",int(phi_max10),"degrees",int(phim),"minutes",round(phis,3),"seconds"
print "answer varies due to rounding off errors"
print "angular position of 1st minimum is",int(phi_min1),"degrees",int(phi_m),"minutes",int(phi_s),"seconds"

angular position of 10th maximum is 3 degrees 7 minutes 30.887 seconds
answer varies due to rounding off errors
angular position of 1st minimum is 0 degrees 9 minutes 23 seconds

Example number 14.3, Page number 14.43

In [41]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew=1.33;      #refractive index of soap
t=5000*10**-10;    #thickness(m)
n0=0;
n1=1;
n2=2;
n3=3;

#Calculation
x=4*mew*t;
lamda1=x/((2*n0)+1);       #for n=0
lamda2=x/((2*n1)+1);       #for n=1
lamda3=x/((2*n2)+1);       #for n=2
lamda4=x/((2*n3)+1);       #for n=3

#Result
print lamda3*10**10,"angstrom lies in the visible region"

5320.0 angstrom lies in the visible region

Example number 14.4, Page number 14.43

In [42]:
#importing modules
import math
from __future__ import division

#Variable declaration
D15=0.59*10**-2;     #diameter of 15th ring(m)
D5=0.336*10**-2;     #diameter of 5th ring(m)
R=1;    #radius(m)
m=10;

#Calculation
lamda=((D15**2)-(D5**2))/(4*m*R);     #wavelength of light(m)

#Result
print "wavelength of light is",int(lamda*10**10),"angstrom"

wavelength of light is 5880 angstrom

Example number 14.5, Page number 14.44

In [43]:
#importing modules
import math
from __future__ import division

#Variable declaration
D10=0.5*10**-2;     #diameter of 10th ring(m)
lamda=5900*10**-10;    #wavelength of light(m)
n=10;

#Calculation
R=D10**2/(4*n*lamda);     #radius of curvature(m)

#Result
print "radius of curvature is",round(R,3),"m"

radius of curvature is 1.059 m

Example number 14.6, Page number 14.44

In [44]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda1=650*10**-9;      #wavelength(m)
lamda2=500*10**-9;      #wavelength(m)
D=1;    #distance(m)
d=0.5*10**-3;     #seperation(m)
n=10;

#Calculation
x=n*lamda1*D/d;    #least distance of the point(m)

#Result
print "least distance of the point is",int(x*10**3),"mm"

least distance of the point is 13 mm

Example number 14.7, Page number 14.45

In [45]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=500*10**-9;    #wavelength(m)
n=10;
D10=2*10**-3;     #diameter(m)

#Calculation
r10=D10/2;    #radius(m)
R=D10**2/(4*n*lamda);
t=r10**2/(2*R);        #thickness(m)

#Result
print "thickness is",t*10**6,"micro m"

thickness is 2.5 micro m

Example number 14.8, Page number 14.45

In [46]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=0.2*10**-3;     #seperation(m)
lamda=550*10**-9;    #wavelength(m)
D=1;     #diameter(m)

#Calculation
beta=lamda*D/d;     #fringe width(m)

#Result
print "fringe width is",beta*10**3,"mm"

fringe width is 2.75 mm

Example number 14.9, Page number 14.45

In [47]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=500*10**-9;    #wavelength(m)
D=2;     #diameter(m)
beta=(5/100)*10**-2;     #fringe width(m)

#Calculation
d=lamda*D/beta;      #separation between slits(m)

#Result
print "separation between slits is",int(d*10**3),"mm"

separation between slits is 2 mm

Example number 14.10, Page number 14.46

In [48]:
#importing modules
import math
from __future__ import division

#Variable declaration
a12=36;       #intensity 1
a22=1;        #intensity 2

#Calculation
a1=math.sqrt(a12);
a2=math.sqrt(a22);
Imin=(a1-a2)**2;     #minimum intensity
Imax=(a1+a2)**2;     #maximum intensity
r=Imax/Imin;

#Result
print "ratio of maximum intensity to minimum intensity is",round(r)

ratio of maximum intensity to minimum intensity is 2.0

Example number 14.11, Page number 14.46

In [51]:
#importing modules
import math
from __future__ import division

#Variable declaration
D5=0.3;      #diameter of 5th ring(cm)
D15=0.62;    #diameter of 15th ring(cm)

#Calculation
D_25=2*(D15**2)-(D5**2);
D25=math.sqrt(D_25);      #diameter of 25th ring(cm)

#Result
print "diameter of 25th ring is",round(D25,4),"cm"

diameter of 25th ring is 0.8239 cm