1: Interference

Example number 1, Page number 30

In [2]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=0.08*10**-2;         #distance between slits(m)
beta=6*10**-4;         #fringe width(m)
c=3*10**8;             #velocity of light(m/sec)
new=8*10**11*10**3;    #frequency(Hz)

#Calculation
lamda=c/new;           #wavelength(m)
D=beta*d/lamda;        #distance of screen from slits(m)

#Result
print "distance of screen from slits is",D,"m"

distance of screen from slits is 1.28 m

Example number 2, Page number 30

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda1=4200*10**-10;    #wavelength(m)
beta1=0.64*10**-2;      #first fringe width(m)
beta2=0.46*10**-2;      #second fringe width(m)

#Calculation
lamda2=lamda1*2*beta2/beta1;    #wavelength of light source(m)

#Result
print "wavelength of light source is",lamda2*10**10,"angstron"

wavelength of light source is 6037.5 angstron

Example number 3, Page number 31

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
Y=1*10**-3;           #distance between slits(m)
D=1;                  #distance between slit and screen(m)
d=1*10**-3;           #point distance(m)
lamda=5893*10**-10;   #wavelength(angston)

#Calculation
delta1=Y*d/D;                #path difference(m)
Pd=2*math.pi*delta1/lamda;   #phase difference(radian)
r=(math.cos(Pd/2))**2;       #ratio of intensity
delta2=lamda/4;              #path difference(m)
W=delta2*D/d;                #distance of point on screen from centre(m)

#Result
print "ratio of intensity is",round(r,4)
print "distance of point on screen from centre is",round(W*10**4,3),"*10**-4 m"
print "answers in the book varies due to rounding off errors"

ratio of intensity is 0.3363
distance of point on screen from centre is 1.473 *10**-4 m
answers in the book varies due to rounding off errors

Example number 4, Page number 32

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

#Variable declaration
I1=10;                       #intensity(Wm**-2)
I2=25;                       #intensity(Wm**-2)

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

#Result
print "ratio of maximum intensity to minimum intensity is",round(ImaxbyImin,3)

ratio of maximum intensity to minimum intensity is 19.727

Example number 5, Page number 32

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

#Variable declaration
ImaxbyImin=9/1;      #ratio of fringes

#Calculation
amaxbyamin=math.sqrt(ImaxbyImin);
#Result
print "ratio of intensity is",

ratio of intensity is

Example number 6, Page number 33

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=500*10**-9;      #wavelength(m)
D=2;                   #distance of screen from slits(m)
l=5*10**-2;            #distance(m)
n=100;                 #number of fringes

#Calculation
beta=l/n;
d=lamda*D/beta;         #distance between slits(m)

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

distance between slits is 2 mm

Example number 7, Page number 33

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

#Variable declaration
d=0.2*10**-3;          #distance between slits(m)
lamda=550*10**-9;      #wavelength(m)
D=1;                   #distance of screen from slits(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 8, Page number 33

In [32]:
#importing modules
import math
from __future__ import division

#Variable declaration
n=10;           
lamda=5460*10**-10;         #wavelength(m)
d=0.1*10**-3;               #distance between slits(m)
D=2;                        #distance of screen from slits(m)

#Calculation
x10=n*lamda*D/d;                 #distance from centre where 10th maximum is obtained(m)
tantheta1=x10/2;                 #angular position of 10th maximum(radian)
tantheta1=tantheta1*180/math.pi; #angular position of 10th maximum(degrees)
x1=lamda*D/(2*d);                #distance from centre where 1st maximum is obtained(m)
tantheta2=x1/2;                  #angular position of 1st maximum(radian)
tantheta2=tantheta2*180/math.pi; #angular position of 1st maximum(degrees)

#Result
print "angular position of 10th maximum is",round(tantheta1,2),"degrees"
print "angular position of 1st maximum is",round(tantheta2,3),"degrees"

angular position of 10th maximum is 3.13 degrees
angular position of 1st maximum is 0.156 degrees

Example number 9, Page number 34

In [36]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda1=650*10**-9;       #wavelength(m)
lamda2=500*10**-9;       #wavelength(m)
n1=10;
n2=13;
D=1;                     #distance(m)
d=0.5*10**-3;            #seperation(m)

#Calculation
x=n1*lamda1*D/d;         #least distance of the point from central maximum(m)

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

 least distance of the point from central maximum is 13 mm

Example number 10, Page number 35

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

#Variable declaration
n=5;
lamda=4800*10**-10;       #wavelength(m)
mew_mewdash=0.3;          

#Calculation
t=n*lamda/mew_mewdash;         #thcikness of glass plate(m)

#Result
print "thcikness of glass plate is",t*10**6,"*10**-6 m"
print "answer given in the book is wrong"

thcikness of glass plate is 8.0 *10**-6 m
answer given in the book is wrong

Example number 11, Page number 35

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

#Variable declaration
v=0.2;         #volume(cc)
a=1*10**4;     #area(cm**2)
r=0;
n=1;
lamda=5.5*10**-5;      #wavelength(cm)
t=2;

#Calculation
d=v/a;       #thickness of film(cm)
mew=n*lamda/(2*t*math.cos(r));      #refractive index of oil

#Result
print "refractive index of oil is",round(mew*10**5,2),"*10**-5"
print "answer given in the book is wrong"

refractive index of oil is 1.38 *10**-5
answer given in the book is wrong

Example number 12, Page number 35

In [53]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew=1.33;        #refractive index
i=35*math.pi/180;      #angle of incidence(radian)
d=5*10**-5;            #thickness(cm)
n1=1;                  #order 
n2=2;                  #order
n3=3;                  #order 
n4=4;                  #order

#Calculation
r=180/math.pi*math.asin(math.sin(i)/mew);     #angle of reflection(degrees)
lamda1=2*mew*d*math.cos(r)/n1;            #wavelength of light for 1st order(cm)
lamda2=2*mew*d*math.cos(r)/n2;            #wavelength of light for 2nd order(cm)
lamda3=2*mew*d*math.cos(r)/n3;            #wavelength of light for 3rd order(cm)
lamda4=2*mew*d*math.cos(r)/n4;            #wavelength of light for 4th order(cm)

#Result
print "wavelength of light for 1st order is",round(lamda1*10**5,1),"*10**-5 cm"
print "answer in the book varies due to rounding off errors"
print "wavelength of light for 2nd order is",round(lamda2*10**5,2),"*10**-5 cm"
print "wavelength of light for 3rd order is",round(lamda3*10**5,2),"*10**-5 cm"
print "wavelength of light for 4th order is",round(lamda4*10**5,1),"*10**-5 cm"

wavelength of light for 1st order is 12.2 *10**-5 cm
answer in the book varies due to rounding off errors
wavelength of light for 2nd order is 6.09 *10**-5 cm
wavelength of light for 3rd order is 4.06 *10**-5 cm
wavelength of light for 4th order is 3.0 *10**-5 cm

Example number 13, Page number 36

In [56]:
#importing modules
import math
from __future__ import division

#Variable declaration
x=15;            #distance(cm)
d=0.005;         #diameter(cm)
lamda=6000*10**-8;     #wavelength(cm)

#Calculation
alpha=d/x;               #angle(radian)
beta=lamda/(2*alpha);    #fringe width(cm)

#Result
print "fringe width is",beta,"cm"

fringe width is 0.09 cm

Example number 14, Page number 36

In [58]:
#importing modules
import math
from __future__ import division

#Variable declaration
alpha=0.01;             #angle(radian)
n=10;
lamda=6000*10**-10;     #wavelength(m)

#Calculation
x=((2*n)-1)*lamda/(4*alpha);     #distance from edge of the wedge(m)

#Result
print "distance from edge of the wedge is",x*10**4,"*10**-4 m"

distance from edge of the wedge is 2.85 *10**-4 m

Example number 15, Page number 36

In [63]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5460*10**-8;      #wavelength(cm)
f=400;            #focal length(cm)
n=5;
mew=1.5;          #refractive index

#Calculation
R=2*f*(mew-1);      #radius(cm)
Dn=math.sqrt(2*((2*n)-1)*lamda*R);    #diameter of 5th fringe(cm)

#Result
print "diameter of 5th fringe is",round(Dn,2),"m"

diameter of 5th fringe is 0.63 m

Example number 16, Page number 37

In [72]:
#importing modules
import math
from __future__ import division

#Variable declaration
t=500*10**-9;      #thickness(m)
f=400;            #focal length(cm)
n1=0;
n2=1;
n3=2;
n4=3;
mew=1.33;          #refractive index

#Calculation
lamda1=4*mew*t/((2*n1)+1);     #wavelength in infrared region(m)
lamda2=4*mew*t/((2*n2)+1);     #wavelength in infrared region(m)
lamda3=4*mew*t/((2*n3)+1);     #wavelength in visible region(m)
lamda4=4*mew*t/((2*n4)+1);     #wavelength in ultraviolet region(m)

#Result
print "wavelength in infrared region is",int(lamda1*10**10),"*10**-10 m"
print "wavelength in infrared region is",round(lamda2*10**10,1),"*10**-10 m"
print "wavelength in visible region is",int(lamda3*10**10),"*10**-10 m"
print "wavelength in ultraviolet region is",int(lamda4*10**10),"*10**-10 m"
print "of all the wavelengths reflected,",int(lamda3*10**10),"angstrom is the wavelength in the visible region"

wavelength in infrared region is 26600 *10**-10 m
wavelength in infrared region is 8866.7 *10**-10 m
wavelength in visible region is 5320 *10**-10 m
wavelength in ultraviolet region is 3800 *10**-10 m
of all the wavelengths reflected, 5320 angstrom is the wavelength in the visible region

Example number 17, Page number 38

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

#Variable declaration
i=60*math.pi/180;       #angle of incidence(radian)
mew=1.33;          #refractive index
t=1.5*10**-6;      #thickness(m)
lamda=5*10**-7;    #wavelength(m)

#Calculation
r=(180/math.pi)*math.asin(math.sin(i)/mew);     #angle of reflection(degrees)
r=round(r,1)*math.pi/180;            #angle of reflection(degrees)
n=2*mew*t*math.cos(r)/lamda;                    #order of interference

#Result
print "order of interference is",int(n)

order of interference is 6

Example number 18, Page number 38

In [82]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew=1.5;          #refractive index
lamda=5890*10**-10;    #wavelength(m)
r=60*math.pi/180;      #angle of reflection(radian)

#Calculation
t=lamda/(2*mew*math.cos(r));       #smallest thickness of the plate(m)

#Result
print "smallest thickness of the plate is",int(round(t*10**10)),"angstrom"

smallest thickness of the plate is 3927 angstrom

Example number 19, Page number 39

In [85]:
#importing modules
import math
from __future__ import division

#Variable declaration
D4=0.4;            #diameter of 4th ring(cm)
D12=0.7;           #diameter of 12th ring(cm)
p1=16;
p2=8;      
n=4;

#Calculation
x=n*p1/(n*p2);
D20=math.sqrt((D4**2)+(x*((D12**2)-(D4**2))));      #diameter of 20th dark ring(cm)

#Result
print "diameter of 20th dark ring is",round(D20,3),"cm"

diameter of 20th dark ring is 0.906 cm

Example number 20, Page number 39

In [89]:
#importing modules
import math
from __future__ import division

#Variable declaration
D10=1.4;           #diameter of 10th ring(cm)
D10_dash=1.27;     #changed diameter of 10th ring(cm)

#Calculation
mew=(D10**2)/(D10_dash**2);      #refractive index of the liquid

#Result
print "refractive index of the liquid is",round(mew,3)

refractive index of the liquid is 1.215

Example number 21, Page number 39

In [99]:
#importing modules
import math
from __future__ import division

#Variable declaration
D25=0.8;       #diameter of 25th ring(cm)
D5=0.3;        #diameter of 5th ring(cm)
p=25-5;
R=100;         #radius of curvature(cm)

#Calculation
Nr=(D25**2)-(D5**2);    #numerator
Dr=4*p*R;               #denominator
lamda=Nr/Dr;            #wavelength of light used(cm)

#Result
print "wavelength of light used is",lamda*10**5,"*10**-5 cm"
print "answer given in the book is wrong"

wavelength of light used is 6.875 *10**-5 cm
answer given in the book is wrong

Example number 22, Page number 40

In [105]:
#importing modules
import math
from __future__ import division

#Variable declaration
w=0.02;            #width(m)
theta=(math.pi/180)*(18+(14/60));      #angle(radian)
n=1;               
lamda=6.56*10**-7;               #wavelength(m)

#Calculation
M=w*math.sin(theta)/(n*lamda);   #total number of lines in the grating 

#Result
print "total number of lines in the grating is",round(M,1)
print "answer given in the book varies due to rounding off errors"

total number of lines in the grating is 9539.3
answer given in the book varies due to rounding off errors

Example number 23, Page number 40

In [110]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5890*10**-10;               #wavelength(m)
mew=1.5;                #refractive index
r=60*math.pi/180;       #angle of reflection(radian)

#Calculation
t=lamda/(2*mew*math.cos(r));     #required thickness of plate(m)

#Result
print "required thickness of plate is",int(round(t*10**10)),"angstrom"

required thickness of plate is 3927 angstrom

Example number 24, Page number 40

In [115]:
#importing modules
import math
from __future__ import division

#Variable declaration
R=1;                 #radius of curvature(m)
n=5;
lamda=5.895*10**-7;         #wavelength(m)
dn=0.3*10**-2;             #diameter of ring(m)

#Calculation
mew=4*R*n*lamda/(dn**2);    #refractive index of liquid

#Result
print "refractive index of liquid is",mew

refractive index of liquid is 1.31

Example number 25, Page number 41

In [118]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=6500;         #wavelength(m)
theta=30*math.pi/180;      #angle(radian)

#Calculation
a=lamda/math.sin(theta);    #value of slit width(angstrom)

#Result
print "value of slit width is",int(a),"angstrom"

value of slit width is 13000 angstrom

Example number 27, Page number 41

In [120]:
#importing modules
import math
from __future__ import division

#Variable declaration
t=500*10**-9;      #thickness(m)
n1=0;
n2=1;
n3=2;
n4=3;
mew=1.33;          #refractive index

#Calculation
lamda1=4*mew*t/((2*n1)+1);     #wavelength in infrared region(m)
lamda2=4*mew*t/((2*n2)+1);     #wavelength in infrared region(m)
lamda3=4*mew*t/((2*n3)+1);     #wavelength in visible region(m)
lamda4=4*mew*t/((2*n4)+1);     #wavelength in ultraviolet region(m)

#Result
print "wavelength in infrared region is",int(lamda1*10**10),"*10**-10 m"
print "wavelength in infrared region is",round(lamda2*10**10,1),"*10**-10 m"
print "wavelength in visible region is",int(lamda3*10**10),"*10**-10 m"
print "wavelength in ultraviolet region is",int(lamda4*10**10),"*10**-10 m"
print "of all the wavelengths reflected,",int(lamda3*10**10),"angstrom is the wavelength in the visible region"

wavelength in infrared region is 26600 *10**-10 m
wavelength in infrared region is 8866.7 *10**-10 m
wavelength in visible region is 5320 *10**-10 m
wavelength in ultraviolet region is 3800 *10**-10 m
of all the wavelengths reflected, 5320 angstrom is the wavelength in the visible region

Example number 28, Page number 42

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
i=60*math.pi/180;       #angle of incidence(radian)
mew=1.33;          #refractive index
t=1.5*10**-6;      #thickness(m)
lamda=5*10**-7;    #wavelength(m)

#Calculation
r=(180/math.pi)*math.asin(math.sin(i)/mew);     #angle of reflection(degrees)
r=round(r,1)*math.pi/180;            #angle of reflection(degrees)
n=2*mew*t*math.cos(r)/lamda;                    #order of interference

#Result
print "order of interference is",int(n)

order of interference is 6

Example number 29, Page number 42

In [121]:
#importing modules
import math
from __future__ import division

#Variable declaration
mew=1.5;          #refractive index
lamda=5890*10**-10;    #wavelength(m)
r=60*math.pi/180;      #angle of reflection(radian)

#Calculation
t=lamda/(2*mew*math.cos(r));       #smallest thickness of the plate(m)

#Result
print "smallest thickness of the plate is",int(round(t*10**10)),"angstrom"

smallest thickness of the plate is 3927 angstrom

Example number 30, Page number 43

In [124]:
#importing modules
import math
from __future__ import division

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

#Calculation
R=Dn**2/(4*n*lamda);     #radius(m)
t=Dn**2/(8*R);           #thickness of air film(m)

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

thickness of air film is 2.5 micro m

Example number 31, Page number 43

In [131]:
#importing modules
import math
from __future__ import division

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

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

#Result
print "wavelength of light is",int(lamda*10**9),"nm"

wavelength of light is 588 nm

Example number 32, Page number 43

In [135]:
#importing modules
import math
from __future__ import division

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

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

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

radius of curvature of lens is 1.059 m

Example number 33, Page number 44

In [138]:
#importing modules
import math
from __future__ import division

#Variable declaration
Dn=0.3*10**-2;       #diameter of 10th ring(m)
R=1;                 #radius of curvature(m)
n=5;
lamda=5.895*10**-7;   #wavelength(m)

#Calculation
mew=4*R*n*lamda/Dn**2;      #refractive index of liquid

#Result
print "refractive index of liquid is",mew

refractive index of liquid is 1.31

Example number 34, Page number 44

In [139]:
#importing modules
import math
from __future__ import division

#Variable declaration
D10=1.4;           #diameter of 10th ring(cm)
D10_dash=1.27;     #changed diameter of 10th ring(cm)

#Calculation
mew=(D10**2)/(D10_dash**2);      #refractive index of the liquid

#Result
print "refractive index of the liquid is",round(mew,3)

refractive index of the liquid is 1.215

Example number 35, Page number 45

In [144]:
#importing modules
import math
from __future__ import division

#Variable declaration
I1=1;
I2=25;      #intensity ratio

#Calculation
A1=math.sqrt(I1);
A2=math.sqrt(I2);        
Imax=(A1+A2)**2;
Imin=(A2-A1)**2;     #intensity ratio
Imax=Imax/4;
Imin=Imin/4;         #dividing by a common factor to get the least ratio

#Result
print "intensity ratio is",int(Imax),":",int(Imin)

intensity ratio is 9 : 4

Example number 36, Page number 45

In [148]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda1=6*10**-5;     #wavelength(cm)
lamda2=4.5*10**-5;      #wavelength(cm)
n1=21;

#Calculation
n2=n1*lamda1/lamda2;     #order

#Result
print "order is",int(n2)

order is 28

Example number 37, Page number 46

In [17]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=51*10**-6;       #wavelength(cm)
D=200;            #separation between screen and slit(cm)
beta=1;           #fringe width(cm)
n=10;

#Calculation
d=lamda*D/beta;      #slit separation(cm)

#Result
print "slit separation is",d*100,"m"

slit separation is 1.02 m

Example number 38, Page number 46

In [155]:
#importing modules
import math
from __future__ import division

#Variable declaration
D=50;            #separation between screen and slit(cm)
x=0.2;           #fringe shift(cm)
d=0.1;           #separation between slits(cm)
mew=1.58;        #refractive index

#Calculation
tow=x*d/(D*(mew-1));     #thickness of mica sheet(cm)

#Result
print "thickness of mica sheet is",round(tow*10**4,3),"*10**-4 cm"

thickness of mica sheet is 6.897 *10**-4 cm

Example number 39, Page number 47

In [161]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5000*10**-8;     #wavelength(cm)
D=50;             #separation between screen and slit(cm)
d=0.05;           #separation between slits(cm)

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

#Result
print "fringe width is",beta,"cm"

fringe width is 0.05 cm

Example number 40, Page number 47

In [175]:
#importing modules
import math
from __future__ import division

#Variable declaration
D=180;             #separation between screen and slit(cm)
d=0.04;            #separation between slits(cm)
beta=0.3;          #fringe width(cm)

#Calculation
lamda=round(beta*d*10**4/D,2);      #wavelength(cm)

#Result
print "wavelength is",int(lamda*10**4),"angstrom"

wavelength is 6700 angstrom

Example number 41, Page number 47

In [181]:
#importing modules
import math
from __future__ import division

#Variable declaration
D=80;             #separation between screen and slit(cm)
d=0.1;            #separation between slits(cm)
beta=0.04;         #fringe width(cm)

#Calculation
lamda=beta*d/D;      #wavelength(cm)

#Result
print "wavelength is",int(lamda*10**8),"angstrom"

wavelength is 5000 angstrom

Example number 42, Page number 48

In [182]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5000*10**-8;     #wavelength(cm)
D=50;             #separation between screen and slit(cm)
d=0.05;           #separation between slits(cm)

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

#Result
print "fringe width is",beta,"cm"

fringe width is 0.05 cm

Example number 43, Page number 48

In [185]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=7*10**-5;     #wavelength(cm)
n=2;
mew=1.33;           #refractive index

#Calculation
t=(((2*n)+1)*lamda/2)/(2*mew);     #thickness of soap film(cm)

#Result
print "thickness of soap film is",round(t*10**5,4),"*10**-5 cm"

thickness of soap film is 6.5789 *10**-5 cm

Example number 44, Page number 49

In [186]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5460*10**-8;     #wavelength(cm)
t=6.3*10**-4;          #thickness(cm)
n=6;

#Calculation
mew=(n*lamda/t)+1;     #refractive index

#Result
print "refractive index is",mew

refractive index is 1.52

Example number 45, Page number 49

In [189]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5000*10**-8;     #wavelength(cm)
n=16;
mew=1.56;     #refractive index

#Calculation
t=n*lamda/(mew-1);          #thickness(cm)

#Result
print "thickness is",round(t*10**4,1),"*10**-4 cm"

thickness is 14.3 *10**-4 cm

Example number 46, Page number 50

In [192]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=6000*10**-8;     #wavelength(cm)
n=1;
mew=1.5;     #refractive index
r=50*math.pi/180;    #angle of refraction(radian)

#Calculation
t=n*lamda/(2*mew*math.cos(r));          #least thickness of glass plate(cm)

#Result
print "least thickness of glass plate is",round(t*10**5,2),"*10**-5 cm"

least thickness of glass plate is 3.11 *10**-5 cm

Example number 47, Page number 50

In [196]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5000*10**-8;     #wavelength(cm)
mew=1.5;     #refractive index
beta=1;      #assume
S=6*beta;

#Calculation
t=S*lamda/(beta*(mew-1));          #least thickness of glass plate(cm)

#Result
print "least thickness of glass plate is",int(t*10**4),"*10**-4 cm"

least thickness of glass plate is 6 *10**-4 cm

Example number 48, Page number 51

In [199]:
#importing modules
import math
from __future__ import division

#Variable declaration
D8=1.42;     #diameter of 8th ring(cm)
D8dash=1.25;     #changed diameter of 8th ring(cm)

#Calculation
mew=D8**2/D8dash**2;     #refractive index of liquid

#Result
print "refractive index of liquid is",round(mew,2)

refractive index of liquid is 1.29

Example number 49, Page number 51

In [206]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=6000*10**-8;     #wavelength(cm)
n=1;
mew=1.33;     #refractive index
r=0*math.pi/180;    #angle of incidence(radian)

#Calculation
t=n*lamda/(2*mew*math.cos(r));          #thickness of thinnest film(cm)

#Result
print "thickness of thinnest film is",round(t*10**5,4),"*10**-5 cm"
print "answer given in the book is wrong"

thickness of thinnest film is 2.2556 *10**-5 cm
answer given in the book is wrong

Example number 50, Page number 51

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

#Variable declaration
lamda=6000*10**-8;     #wavelength(cm)
Dm=0.65;     #diameter of 8th ring(cm)
Dn=0.35;     #changed diameter of 8th ring(cm)

#Calculation
R=(Dm**2-Dn**2)/(4*lamda);     #radius of curvature of lens(cm)

#Result
print "radius of curvature of lens is",int(R),"cm"
print "answer given in the book is wrong"

radius of curvature of lens is 1250 cm
answer given in the book is wrong

Example number 51, Page number 52

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
Da=1.45;     #diameter of 12th ring in air medium(cm)
Dl=1.25;     #diameter of 12th ring in liquid(cm)

#Calculation
mew=Da**2/Dl**2;    #refractive index of liquid

#Result
print "refractive index of liquid is",mew

refractive index of liquid is 1.3456

Example number 52, Page number 52

In [27]:
#importing modules
import math
from __future__ import division

#Variable declaration
m1=15;
n=5;
m2=25;
D15=0.62;     #diameter of 15th ring(cm)
D5=0.3;       #diameter of 5th ring(cm)

#Calculation
x=D15**2-D5**2;
y=m1-n;
z=m2-n;
r=4*z/(4*y);     
D25=math.sqrt((r*x)+(D5**2));     #diameter of 25th ring(cm)

#Result
print "diameter of 25th ring is",round(D25,3),"cm"

diameter of 25th ring is 0.824 cm

Example number 53, Page number 53

In [31]:
#importing modules
import math
from __future__ import division

#Variable declaration
lamda=5890*10**-8;     #wavelength(cm)
Dm=0.590;     #diameter of 8th ring(cm)
Dn=0.336;     #changed diameter of 8th ring(cm)
m=15;
n=5;

#Calculation
R=(Dm-Dn)/(4*lamda*(m-n));     #radius of curvature of lens(cm)

#Result
print "radius of curvature of lens is",round(R,1),"cm"

radius of curvature of lens is 107.8 cm

Example number 54, Page number 53

In [34]:
#importing modules
import math
from __future__ import division

#Variable declaration
R=70;               #radius of curvature of lens(cm)
n=10;
Dn=0.433;           #diameter of 10th dark ring(cm)

#Calculation
lamda=Dn**2/(4*R*n);     #wavelength of light(cm)

#Result
print "wavelength of light is",round(lamda*10**5,3),"*10**-5 cm"
print "answer given in the book varies due to rounding off errors"

wavelength of light is 6.696 *10**-5 cm
answer given in the book varies due to rounding off errors