Chapter 1 Interference of light

Example 1.1 Page no 35

In [7]:
#Given
I1=9
I2=4.0

#Calculation
import math
I=I1/I2
i=math.sqrt(I)
Imax=((i+1)/(i-1))**2

#Result
print"Ratio of maximum intensity of the fringe system is",Imax,":1"

Ratio of maximum intensity of the fringe system is 25.0 :1

Example 1.2 Page no 36

In [9]:
#Given
a=4
b=2

#Calculation
amax=a+b
amin=a-b
I=amax**2/amin**2

#Result
print"Ratio of maximum to minimum intensity is", I

Ratio of maximum to minimum intensity is 9

Example 1.3 Page no 36

In [24]:
#Given
I=0.6
a=0.4
I2=0.4
a1=1.6

#Calculation
import math
A=(I-a1-a)/(2.0*math.sqrt(a1*a))
A1=math.acos(A)*180.0/3.14

#Result
print"Minimum phase difference is", round(A1,0),"Degree"

Minimum phase difference is 151.0 Degree

Example 1.4 Page no 36

In [28]:
#Given
d=0.5*10**-3                         #m
lembda=5890*10**-10                   #m
D=0.5                                 #m

#Calculation
B=D*lembda/d

#Result
print"Width of fringes is", B*10**3,"10**-3 m"

Width of fringes is 0.589 10**-3 m

Example 1.5 Page no 36

In [34]:
#Given
lembda=5100*10**-10                          #m
D=2
x=0.02
n=10.0

#Calculation
B=x/n
d=D*lembda/B

#Result
print"Double slit seperation is", d*10**5,"*10**-5 m"

Double slit seperation is 51.0 *10**-5 m

Example 1.6 Page no 36

In [38]:
#Given
B=0.31*10**-3                       #m
d=1.9*10**-3
D=1

#Calculation
lembda=B*d/D

#Result
print"Wavelength of light is",lembda*10**10,"A"

Wavelength of light is 5890.0 A

Example 1.7 Page no 37

In [41]:
#Given
n=10
D=0.04                               #m
lembda=5890*10**-10
d=2*10**-3                          #m

#Calculation
x10=n*D*lembda/d

#Result
print"Position of tenth bright fringe is",x10*10**4,"*10**-4 m"

Position of tenth bright fringe is 1.178 *10**-4 m

Example 1.8 Page no 37

In [46]:
#Given
L=5890*10**-10                  #m
a=0.05
b=0.75
B=9.424*10**-4

#Calculation
D=a+b
B1=L*D/B

#Result
print"Distance is", B1*10**4,"*10**-4 m"

Distance is 5.0 *10**-4 m

Example 1.9 Page no 37

In [51]:
#Given
a=0.10
b=1
l=5900*10**-10
A=22
u=1.5

#Calculation
D=a+b
B=L*D*180*7/(2*a*(u-1)*A)

#Result
print"Fringe width is", round(B*10**5,0),"*10**-5 m"

Frige width is 37.0 *10**-5 m

Example 1.10 Page no 37

In [57]:
#Given
u=1.45
l=5890*10**-10                    #m

#Calculation
t=5*l/(u-1)

#Result
print"Thickness is", round(t*10**6,3)*10**-6,"m"

Thickness is 6.544e-06 m

Example 1.11 Page no 38

In [11]:
#Given
a=0.25                          #m
b=1.75
L=5*10**-7
u=1.50
B=0.2*10**-3

#Calculation
D=a+b
d=L*D/B
A=(L*D)/(B*2*a*(u-1))

#Result
print"Angle at the vertex is", A,"Radian"

Angle at the vertex is 0.02 Radian

Example 1.12 Page no 38

In [20]:
#Given
B=0.0135                   #cm
a=50
b=50.0
u=1.5
A=179                       #Degree

#Calculation
import math
D=a+b
L=(2*a*(u-1)*B*math.pi)/(D*360)

#Result
print"Wavelength of light is", round(L*10**8,0),"A"

Wavelength of light is 5890.0 A

Example 1.13 Page no 38

In [29]:
#Given
d1=0.75
d=1
b=0.087

#Calculation
B=d/d1
B1=B*b

#Result
print"Fringe width is", B1,"mm"

Fringe width is 0.116 mm

Example 1.14 Page no 39

In [37]:
#Given
u=1.50
a=0.10                             #m

#Calculation
import math
d=(2*(u-1)*a*math.pi)/90.0

#Result
print"Separation between coherent sources is",round(d*10**2,2),"*10**-2 m"

Separation between coherent sources is 0.35 *10**-2 m

Example 1.15 Page no 39

In [38]:
#Given
t=6.3*10**-6                    #m
L=5460*10**-10
n=6

#Calculattion
u=((n*L)/t)+1

#Result
print"Refractive index is",u

Refractive index is 1.52

Example 1.16 Page no 39

In [40]:
#Given
t=3.4*10**-6                         #m
L=5893*10**-10

#Calculation
u=1+((4*L)/t)

#Result
print"Refractive index is",round(u,2)

Refractive index is 1.69

Example 1.17 Page no 39

In [41]:
#Given
L=6000*10**-10
t=3.6*10**-5
n=30

#Calculation
u=1+((n*L)/t)

#Result
print"Refractive index of the sheet is",u

Refractive index of the sheet is 1.5

Example 1.18 Page no 40

In [44]:
#Given
n=2
D=1.2
d=3*10**-5
x2=45*10**-3

#Calculation
L=x2*d/(D*n)

#Result
print"lembda is",L*10**10,"A"

lembda is 5625.0 A

Eaxmple 1.19 Page no 40

In [47]:
#Given
L1=6.1*10**-5
L2=6.0*10**-5
u=4/3.0
I=4/5.0

#Calculation
import math
t=L1*L2/((L1-L2)*2*math.sqrt(u**2-I**2))

#Result
print"Thickness is",round(t,4),"cm"

Thickness is 0.0017 cm

Example 1.20 Page no 41

In [52]:
#Given
u=1.5
L=5890*10**-10
n=1
r=60                    #degree
a=0.5

#Calculation
t=n*L/(2*u*a)

#Result
print"Smallest thickness of the plate is", round(t*10**10,0),"*10**-10 m"

Smallest thickness of the plate is 3927.0 *10**-10 m

Example 1.21 Page no 41

In [59]:
#Given
L=5890*10**-10
n=8
a=1/2.0
b=1.5

#Calculation
r=math.sqrt(1-(a/b)**2)
t=n*L/(2*b*r)

#Result
print"Film thickness is", round(t*10**6,3)*10**-6,"m"

Film thickness is 1.666e-06 m

Example 1.22 Page no 41

In [73]:
#Given
L=5*10**-7                        #m
t=1.5*10**-6
u=4/3.0
A=0.7604

#Calculation
import math
r=(math.sin(60*3.14/180.0))/u
n=2*u*t*A/L

print"Order of dark band is", round(n,0)

Order of dark band is 6.0

Example 1.23 Page no 42

In [76]:
#Given
x=0.15
L=6000*10**-10
A=0.05*10**-3

#Calculation
B=L*x/(2*A)

#Result
print"Fringe width is",B*10**4,"*10**-4 m"

Fringe width is 9.0 *10**-4 m

Example 1.24 Page no 42

In [83]:
#Given
B=0.5*10**-2
u=1.40
a=10
b=22

#Calculation
L=2*a*b*u*B/(60*60*180*7)

#Result
print"Wavelength of light is", round(L*10**10,0),"*10**-10 m"

Wavelength of light is 6790.0 *10**-10 m

Example 1.25 Page no 43

In [88]:
#Given
x=10**-2
m=10
L=6000*10**-10

#Calculation
import math
A=m*L/(2*x)
A1=A*180*60*60/(math.pi)

#Result
print"Angle of wedge is", round(A1,1),"Seconds"

Angle of wedge is 61.9 Seconds

Example 1.26 Page no 43

In [96]:
#Given
u=1.4
t=0.001
L1=4000.0*10**-8
L2=5000.0*10**-8

#Calculation
import math
r=math.sqrt(1-1/(2*u**2))
n1=2*u*t*r/L1
n2=2*u*t*r/L2
n=n1-n2

#Result
print"Number of dark bands is", round(n,0)

Number of dark bands is 12.0

Example 1.27 Page no 44

In [102]:
#Given
L=5890*10**-10
d=10**-2
u=1
n=3

#Calculation
import math
R=d**2*math.cos(30*3.14/180.0)
R1=R/(4*n*L)

#Result
print"Radius of the lens is", round(R1,2),"m"

Radius of the lens is 12.25 m

Example 1.28 Page no 44

In [107]:
#Given
n=8
dn=0.72*10**-2
R=3
u=1

#Calculation
L=dn**2/((2*n-1)*2*R)

#Result
print"Wavelength of light is", L*10**10,"*10**-10 m"

Wavelength of light is 5760.0 *10**-10 m

Example 1.29 Page no 44

In [119]:
#Given
n=5
L=5400*10**-8
R1=100.0
R2=100.0
n1=15

#Calculation
import math
r=math.sqrt((n*L)/(1/R1+1/R2))
r1=math.sqrt((n1*L)/(1/R1+1/R2))
R=r1-r

#Result
print"Distance between 5th and 15th dark ring is", round(R,4),"cm"

Distance between 5th and 15th dark ring is 0.0851 cm

Example 1.30 Page no 45

In [121]:
#Given
d=0.25                       #cm
dair=0.30

#Calculation
u=(dair/d)**2

#Result
print"Refractive index is",u

Refractive index is 1.44

Example 1.31 Page no 45

In [129]:
#Given
R1=3.0                       #m
R2=4.0
n=13
L=6*10**-7

#Calculation
import math
r=math.sqrt((2*n-1)*L/((1/R1-1/R2)*2.0))
D=2*r

#Result
print" Diameter of the 13th bright ring is",round(D,3),"m"

 Diameter of the 13th bright ring is 0.019 m

Example 1.32 Page no 45

In [135]:
#Given
u=1
d1=0.25
d2=0.30
c=3*10**8

#Calculation
V=((d1/d2)**2)*c

#Result
print"Velocity of light is",round(V*10**-8,2),"*10**8 m/s"

Velocity of light is 2.08 *10**8 m/s

Example 1.33 Page no 46

In [140]:
#Given
n=5
a=25
m=20
R=100
dn=0.3
d=0.8

#Calculation
L=(d**2-dn**2)/(4*R*m)

#Result
print"Wavelength is", L*10**8,"*10**-8 cm"

Wavelength is 6875.0 *10**-8 cm

Example 1.34 Page no 46

In [145]:
#Given
n=4
a=12
m=8.0
d12=0.700
dn=0.400
n1=20

#Calculation
import math
R=(d12**2-dn**2)/m
d20=math.sqrt(n1*R)

#Result
print"Diameter of 20th dark ring is", round(d20,3),"cm"

Diameter of 20th dark ring is 0.908 cm

Example 1.35 Page no 46

In [149]:
#Given
n=3
a=23
m=20
R=50
d=0.501
dn=0.181

#Calculation
L=(d**2-dn**2)/(4*m*R)

#Result
print"Wavelength is", L*10**8,"*10**-8 cm"

Wavelength is 5456.0 *10**-8 cm

Example 1.36 Page no 47

In [154]:
#Given
d=0.295*10**-3
n=100.0

#Calculation
L=(2*d)/n

#Result
print"Wavelength of light is", L*10**9,"*10**-9 m"

Wavelength of light is 5900.0 *10**-9 m

Example 1.37 Page no 47

In [155]:
#Given
L=5000.0*10**-10
d=0.1*10**-3

#Calculation
n=2*d/L

#Result
print"Number of fringes is",n

Number of fringes is 400.0

Example 1.38 Page no 47

In [161]:
#Given
L=5890*10**-10
d=0.289*10**-3

#Calculation
L1=L**2/(2*d)

#Result
print"Difference in wavelength is",  round(L1*10**10,0)*10**-10,"m"

Difference in wavelength is 6e-10 m

Example 1.39 Page no 47

In [166]:
#Given
u=1.50
L=5890*10**-10
m=10

#Calculation
t=m*L/(2*(u-1))

#Result
print"Thickness of the film is",t*10**8,"*10**-8 m"

Thickness of the film is 589.0 *10**-8 m

Example 1.40 Page no 48

In [167]:
#Given
n=150
L=4000*10**-10
l=0.20

#Calculation
u=1+(n*L/(2*l))

#Result
print"Refractive index is",u

Refractive index is 1.00015

Example 1.41 Page no 48

In [172]:
#Given
u=1.45
n=6.5
L=5890*10**-10

#Calculation
t=n*L/(2*(u-1))

#Result
print"Thickness is", round(t*10**6,3),"*10**-6 m"

Thickness is 4.254 *10**-6 m

Example 1.42 Page no 48

In [176]:
#Given
L1=5896*10**-8
L2=5890*10**-8

#Calculation
d=L1*L2/(2*(L1-L2))

#Result
print"Distance is",round(d,5),"cm"

Distance is 0.02894 cm