# Chapter 1: Interference¶

## Example 1.1, Page 1.40¶

In [8]:
 # Given
l = 6.6e-7 # wavelength of light in meter
L = 1.32e-5 # coherence length in meter

#Calculation
coherence_time = L / (3 * 10 ** 8)#calculation for coherence time

#Result
print "Coherence time = %.1e sec"%coherence_time

Coherence time = 4.4e-14 sec


## Example 1.2, Page 1.40¶

In [10]:
# Given
l = 5.896e-7 # wavelength of light in meter
L = 2.945e-2 # coherence length in meter

#Calculations
coherence_time = L / (3 * 10**8) # calculation for coherence time
n = L / l                         # calculation for number of oscillations

#Results
print "Coherence time = %.3e sec."%coherence_time
print "No. of oscillations = %.2e"%n

Coherence time = 9.817e-11 sec.
No. of oscillations = 4.99e+04


## Example 1.3, Page 1.40¶

In [11]:
# Given
l = 6.058e-7 # wavelength of light in meter
L = 0.2 # coherence length in meter

#Calculations
line_width = (l**2) / L#calculation for line width
f = (3 * 10**8) / l       # calculation for frequency
f_stability = f_spread / f # calculation for frequency stability
coherence_time = L / (3 * 10 ** 8) # calculation for coherence time

#Results
print("Coherence time = %.3e sec"%coherence_time)
print("Line width = %.3e meter"%line_width)
print("Frequency stability = %.1e"%f_stability)  #incorrect answer in the textbook

Coherence time = 6.667e-10 sec
Line width = 1.835e-12 meter
Frequency stability = 3.0e-06


## Example 1.4, Page 1.41¶

In [12]:
# Given
lambda_D = 5.5e-13 # Doppler width of orange light in meter
l = 6.058e-7 # wavelength of light in meter

#Calculation
coherence_length = (l ** 2) / lambda_D# calculation for coherence light

#Result
print("Coherence length = %.4f meter"%coherence_length)

Coherence length = 0.6673 meter


## Example 1.5, Page 1.41¶

In [1]:
# Given
lambda1 = 5.461e-7 # wavelength of light emitted by mercury vapour lamp in meter
band_width1 = 6e8 # band width for mercury vapour lamp in Hz
lambda2 = 6.328e-7 # the operating wavelength of light for He Ne laser
band_width2 = 1e6 # band width for laser in Hz

#Calculations
delta_lambda1 = (lambda1**2 * band_width1) / 3e8 # calculation for difference between two wavelength for mercury vapour
delta_L1 = lambda1**2 / delta_lambda1 # calculation for coherence length for mercury vapour lamp
delta_lambda2 = (lambda2**2 * band_width2) / 3e8 # calculation for difference between two wavelength for He Ne laser
delta_L2 = lambda2**2 / delta_lambda2 # calculation for coherence length for He Ne laser
R = delta_L1/delta_L2 # calculation for ratio of coherence length of mercury vapour lamp to the coherence length of He Ne laser

#Result
print("The ratio of coherence length of mercury vapour lamp to the coherence length of He Ne laser = 1:%d"%(1./R))
#Answer differes due to rounding-off values

The ratio of coherence length of mercury vapour lamp to the coherence length of He Ne laser = 1:600


## Example 1.6, Page 1.42¶

In [2]:
# Given
band_width = 3000 # band width of laser in hertz

#Calculation
coherence_length = (3 * 10 ** 8) / band_width#calculation for coherence length

#Result
print("Coherence length of laser = %.f meter"%(coherence_length))

Coherence length of laser = 100000 meter


## Example 1.7, Page 1.42¶

In [31]:
# Given
l = 6.328e-7 # wavelength of monochromatic light in meter
t = 10**-10 # chopping time in sec

#Calculations
coherence_length = (3 * 10 ** 8) * t # calculation for coherence length of monochromatic light
band_width = 1 / t # calculation for band width
line_width = ((l ** 2) * band_width) / (3 * 10 ** 8) # calculation for line width

#Result
print("Coherence length of monochromatic light = %.e meter. \nband width = %.f Hz. \nline width = %.4f A."%(coherence_length, band_width, line_width*1e10))

Coherence length of monochromatic light = 3e-02 meter.
band width = 10000000000 Hz.
line width = 0.1335 A.


## Example 1.8, Page 1.42¶

In [32]:
# Given
l = 6.438e-7 # wavelength of red cadmium line in meter
L = 3.8e-1 # coherence length in meter

#Calculations
coherence_time = L / (3 * 10 ** 8)# calculation for coherence time
spectral_line_width = (l**2) / L # calculation for spectral line width

#Result
print("Coherence time of red cadmium line = %.3e sec. \nSpectral line width = %.2e meter."%(coherence_time,spectral_line_width))

Coherence time of red cadmium line = 1.267e-09 sec.
Spectral line width = 1.09e-12 meter.


## Example 1.9, Page 1.43¶

In [11]:
from math import sqrt
from sympy import *

# Given
ratio = 16 # ratio of intensities of two waves

#Calculation
a1 = sqrt(ratio) # by the formula amplitude = sqrt(intensity)
a2 = 1
R = ((a1 + a2) ** 2) / ((a1 - a2) ** 2)# calculation for ratio of maximum intensity with minimum intensity
R = nsimplify(R)

#Result
print "Ratio of maximum intensity with minimum intensity =",R

Ratio of maximum intensity with minimum intensity = 25/9


## Example 1.10, Page 1.43¶

In [28]:
# Given
d = 0.0001 # distance between two slits in meter
Beta = 0.005 # width of the fringes formed in meter
D = 1 # distance between slit and screen in meter

#Calculation
l = (Beta * d) / D # calculation for wavelength of light = %e meter

#Result
print("Wavelength of light = %.f A. "%(l*1e10))

Wavelength of light = 5000 A.


## Example 1.11, Page 1.43¶

In [12]:
from math import pi

# Given
alpha = pi / 180 # angle of bi prism in radian
mu = 1.5 # refractive index of biprism
a = 0.4 # distance of bi prism from slit in meter
b = 0.6 # distance of bi prism from screen in meter
l = 5.893e-7 # wavelength of light in meter

#Calculation
D = a + b # calculation for distance between slits and screen
fringe_width = (l * D) / (2 * a * (mu - 1) * alpha) # calculation for fringe width

#Result
print("Fringe width = %.3e meter."%(fringe_width))

Fringe width = 8.441e-05 meter.


## Example 1.12, Page 1.44¶

In [48]:
from math import sqrt

# Given
d1 = 4.05e-3 # distance between slits in first position in meter
d2 = 2.90e-3 # distance between slits in second position in meter
l = 5.893e-7 # wavelength of light in meter
D = 1 # distance between slit and screen

#Calculations
d = sqrt(d1 * d2)# calculation for distance between fringe
fringe_width = (l * D) / d # calculation for fringe width

#Result
print("Fringe width = %.3f mm"%(fringe_width*1000))

Fringe width = 0.172 mm


## Example 1.13, Page 1.44¶

In [49]:
from math import floor

# Given
fringe_width = 3.42e-4 # fringe width in meter
mu = 1.542 # refractive index of glass
Xn = 2.143e-3 # shift of central fringe in meter
l = 5.89e-7 # wavelength of light in meter

#Calculations
n = Xn / fringe_width # calculation for order of the fringe
t = (floor(n) * l) / (mu - 1) # calculation for thickness of the glass

#Result
print("Thickness of glass sheet = %.2e meter. "%t)

Thickness of glass sheet = 6.52e-06 meter.


## Example 1.14, Page 1.45¶

In [50]:
# Given
fringe_width = 9e-4 # fringe width in meter
a = 0.1 # distance of bi prism from slit in meter
b = 0.9 # distance of bi prism from screen in meter
l = 5.896e-7 # wavelength of light in meter

#Calculation
D = a + b # calculation for distance between slits and screen
d = (l * D) / fringe_width # calculation for distance between coherent sources

#Result
print("Distance between coherent sources = %.2e meter. "%d)

Distance between coherent sources = 6.55e-04 meter.


## Example 1.15, Page 1.45¶

In [16]:
from math import pi,degrees

# Given
fringe_width = 0.0135 # fringe width in meter
a = 0.5 # distance of bi prism from slits in meter
b = 0.5 # distance of bi prism from screen in meter
mu = 1.5 # refractive index of bi prism
alpha = pi / 360 # angle of bi prism in radian

#Calculations
D = a + b # calculation for distance between slits and screen
l = (2. * a * (mu - 1) * alpha * fringe_width) / D # calculation for wavelength of light = %e meter

#Result
print("Wavelength of light = %.f A "%(l*1e8))
#Answer differs due to rounding-off errors

Wavelength of light = 5890 A


## Example 1.16, Page 1.45¶

In [21]:
from math import pi

# Given
a = 45 # distance between slit and bi prism in cm
alpha = pi / 180 # angle of bi prism in radian
Mu = 1.5 # refractive index of bi prism
fringe_width = 15.6e-3 # fringe width in meter
D = 90      #cm

#Calculations
d2 = (2*a*(Mu-1)*alpha) # calculation for distance between screen and slit
l = (fringe_width * d2) / D # calculation for wavelength

#Result
print("Wavelength of light = %.f A."%(l/1e-8))
#Answer differs due to rounding-off errors

Wavelength of light = 13614 A.


## Example 1.17, Page 1.45¶

In [15]:
# Given
D = 1.20 # distance between source and eye piece in meter
Xn = 1.9e-2 # distance move by eye piece for 20 fringe in meter
n = 20 # no. of fringes
d = 6e-4 # distance between slits in meter

#Calculation
l = (Xn * d) / (D * n)# calculation for wavelength

#Result
print("Wavelength of light = %.f A."%(l*1e10))

Wavelength of light = 4750 A.


## Example 1.18, Page 1.46¶

In [16]:
from math import floor

# Given
lambda1 = 5.890e-7 # wavelength of first light in meter
lambda2 = 4.358e-7 # wavelength of second light in meter
n1 = 40 # no. of fringes observed in the field of in first case

#Calculation
n2 = (n1 * lambda1) / lambda2 # by using formula n1*lambda1=n2*lambda2

#Result
print("No. of fringes observed in field of view in second case = %d. "%(floor(n2)))

No. of fringes observed in field of view in second case = 54.


## Example 1.19, Page 1.46¶

In [97]:
from math import cos

# Given
l = 5.893e-7 # wavelength of light in meter
Mu = 1.42 # refractive index of soap film
i = 0 # incidence angle in radian
r = 0 # refracted angle in radian
n = 1 # for smallest thickness

#Calculations
t1 = ((2 * n - 1) * l) / (4 * Mu * cos(r)) # calculation for east thickness of soap film for bright fringe
t2 = (n * l) / (2 * Mu * cos(r)) # calculation for east thickness of soap film for dark fringe

#Result
print("Least thickness of soap film -\n (a) For bright fringe = %.3e mm. \n (b) For dark fringe = %.3e mm."%(t1*1000,t2*1000))

Least thickness of soap film -
(a) For bright fringe = 1.038e-04 mm.
(b) For dark fringe = 2.075e-04 mm.


## Example 1.20, Page 1.46¶

In [98]:
from math import cos,pi,sin,asin

# Given
l = 5.89e-7 # wavelength of light in meter
Mu_o = 1.4 # refractive index of oil film
Mu_w = 1.33 # refractive index of water
i = pi / 6 # incidence angle in radian
n = 6 # no. of fringes seen

#Calculation
r = asin(sin(i) / Mu_o) # calculation for angle of refraction
t = (n * l) / (2 * Mu_o * cos(r)) # calculation for thickness of film

#Result
print("Thickness of oil film = %.3e mm."%(t*1000))

Thickness of oil film = 1.351e-03 mm.


## Example 1.21, Page 1.47¶

In [99]:
from math import cos

# Given
l = 6e-7 # wavelength of light in meter
Mu = 1.463 # refractive index of soap film
i = 0 # incidence angle in radian
r = 0 # refracted angle in radian
n = 1 # for smallest thickness

#Calculation
t = ((2 * n - 1) * l) / (4 * Mu * cos(r)) # calculation for least thickness of soap film for bright fringe

#Result
print("Least thickness of soap film for bright fringe = %.3e mm. "%(t*1000))

Least thickness of soap film for bright fringe = 1.025e-04 mm.


## Example 1.22, Page 1.47¶

In [100]:
from math import cos,pi,sin

# Given That
l = 5.89e-7 # wavelength of light
Mu_o = 1.46 # refractive index of oil film
i = pi / 6 # incidence angle in radian
n = 8 # no. of fringe is seen

#Calculations
r = asin(sin(i) / Mu_o) # calculation for angle of refraction
t = (n * l) / (2 * Mu_o * cos(r)) # calculation for thickness of oil film

#Result
print("Thickness of oil film = %.2e mm. "%(t*1000))

Thickness of oil film = 1.72e-03 mm.


## Example 1.23, Page 1.47¶

In [24]:
from math import cos,pi,floor

# Given That
lambda1 = 4e-7 # max. wavelength of light in meter
lambda2 = 5e-7 # min. wavelength of light in meter
Mu = 1.4 # refractive index of soap film
i = pi / 4 # incidence angle in radian
t = 1e-5 # thickness of oil film in meter

#Calculations
r = asin(sin(i) / Mu) # calculation for angle of refraction
n1 = (2 * Mu * t * cos(r)) / lambda1 # calculation for no. of dark bands seen in the case of max. wavelength
n2 = (2 * t * Mu * cos(r)) / lambda2 # calculation for no. of dark seen in the case of min. wavelength
n = floor(n1) - floor(n2) # claculation for no. of dark bands seen between wavelengths

#Result
print("No. of dark bands seen between wavelengths = %d"%n)

No. of dark bands seen between wavelengths = 12


## Example 1.24, Page 1.48¶

In [104]:
from math import cos,pi

# Given
l = 5.89e-7 # wavelength of light in meter
Mu = 1.5 # refractive index of soap film
r = pi / 3 # refracted angle in radian
n = 1 # for smallest thickness

#Calculation
t = (n * l) / (2 * Mu * cos(r)) # calculation for least thickness of soap film for bright fringe

#Result
print("Least thickness of soap film for bright fringe = %.3e meter "%t)

Least thickness of soap film for bright fringe = 3.927e-07 meter


## Example 1.25, Page 1.48¶

In [105]:
from math import cos,pi,sin

# Given That
lambda1 = 6.1e-7 # max. wavelength of light in meter
lambda2 = 6e-7 # min. wavelength of light in meter
Mu = 1.333 # refractive index of  film
i = pi / 4 # incidence angle in radian

#Calculation
r = asin(sin(i) / Mu) # calculation for angle of refraction
n = lambda2 / (lambda1 - lambda2) # calculation for no. of bright band
t = (n * lambda1) / (2 * Mu * cos(r)) # calculation for thickness of the film

#Result
print("Thickness of the film = %.2e meter "%t)

Thickness of the film = 1.62e-05 meter


## Example 1.26, Page 1.49¶

In [106]:
from math import cos

# Given
l = 6e-7 # wavelength of light in meter
Mu = 1.463 # refractive index of soap film
i = 0 # incidence angle in radian
r = 0 # refracted angle in radian
n = 1 # for smallest thickness

#Calculation
t = ((2 * n - 1) * l) / (4 * Mu * cos(r)) # calculation for thickness of soap film

#Result
print("\n Least thickness of soap film for bright fringe = %.3e meter. "%t)

 Least thickness of soap film for bright fringe = 1.025e-07 meter.


## Example 1.27, Page 1.49¶

In [127]:
from math import cos,sin,asin,pi,degrees,radians

# Given
lambda1 = 6.1e-7 # max. wavelength of light in meter
lambda2 = 6e-7 # min. wavelength of light in meter
Mu = 4. / 3 # refractive index of film
i = asin(4. / 5) # incidence angle in radian

#Calculation
r = asin(sin(i) / Mu)*180/pi # calculation for angle of refraction
n = lambda2 / (lambda1 - lambda2) # calculation for order of fringe
t = (n * lambda1) / (2 * Mu * cos(r*pi/180)) # calculation for thickness of film

#Result
print("Thickness of the film = %.3e mm. "%(t*1000))

Thickness of the film = 1.716e-02 mm.


## Example 1.28, Page 1.50¶

In [128]:
# Given
l = 5.893e-7 # wavelenth of light in meter
n = 20 # no. of interference fringes are observed
Mu = 1 # refractive index of air
i = 0 # incidence angle in radian
r = 0 # refracted angle in radian

#Calculation
t = (n * l) / (2 * Mu) # calculation for thickness of fringe

#Result
print("Thickness of wire = %.3e mm. "%(t*1000))

Thickness of wire = 5.893e-03 mm.


## Example 1.29, Page 1.50¶

In [140]:
# Given
lamda = 6e-7 # wavelength of light in meter
Mu = 1 # refractive index of air film
l = 0.06e-3 # diameter of wire in meter
L = 0.15 # distance of wire from edge in meter

#Calculation
theta = l / L #calculation for theta
fringe_width = (lamda * L)/ (2 * Mu * l) # calculation for fringe width

#Result
print("Fringe width = %.1e mm."%fringe_width)

Fringe width = 7.5e-04 mm.


## Example 1.30, Page 1.51¶

In [33]:
# Given
l = 4.56e-7 # wavelength of light in meter
theta = 1.9e-4 # angle of wedge in radian
Mu = 1 # refractive index of air

#Calculation
fringe_width = l / (2 * Mu * theta)# calculation for fringe width

#Result
print("Fringe width = %.1f mm."%(fringe_width*1000))

Fringe width = 1.2 mm.


## Example 1.31, Page 1.51¶

In [141]:
# Given
lamda = 6e-7 # wavelength of light in meter
Mu = 1 # refractive index of air film
l = 0.03*10**-3 # diameter of wire in meter
L = 0.15 # distance of wire from edge in meter
i = 0 # incidence angle in radian
r = 0 # refracted angle in radian

#Calculation
theta = l / L # calculation for theta
fringe_width = lamda / (2 * Mu * theta) # calculation for fringe width

#Result
print("Fringe width = %.1f mm."%(fringe_width*1000))

Fringe width = 1.5 mm.


## Example 1.32, Page 1.51¶

In [142]:
# Given
l = 5.890e-7 # wavelength of light in meter
theta = 1e-2 # angle of wedge in radian
n = 12 # no. of dark fringe
Mu = 1 # refractive index of air
i = 0 # incidence angle in radian
r = 0 # refracted angle in radian

#Calculatiom
x = ( n * l) / (2 * theta) # calculation for distance

#Result
print("Distance = %.2f mm. "%(x*1000))

Distance = 0.35 mm.


## Example 1.33, Page 1.52¶

In [143]:
from math import pi

# Given
l = 5.5e-7 # wavelength of light in meter
w = 2e-5 # fringe width in meter
Mu = 1.5 # refractive index of film
i = 0 # incidence angle in radian
r = 0 # refracted angle in radian

#Calculation
theta = l / (2 * Mu * w)# calculation for the angle of the film

#Result
print("Angle of wedge = %.3f degree. "%(theta * 180/pi))

Angle of wedge = 0.525 degree.


## Example 1.34, Page 1.52¶

In [39]:
# Given
d1 = 5.9e-3 # diameter of 15th ring in meter
d2 = 3.36e-3 # diameter of 5th ring in meter
R = 1 # radius of the plano-convex lens in meter

#Calculations
p = 15 - 5
l = ((d1**2) - (d2**2)) / (4 * p * R) # calculation for wavelength of light

#Result
print("Wavelength of light = %.f A."%(l*1e10))

Wavelength of light = 5880 A.


## Example 1.35, Page 1.52¶

In [145]:
# Given
d1 = 2e-3 # diameter of 10th ring in meter
d2 = 3e-3 # diameter of 20th ring in meter
f = 0.9 # focal length of the plano-convex lens in meter
mu = 1.5 # refractive index of lens

#Calculations
p = 20 - 10
R = (f * (mu - 1)) # calculation for radius of convex surface of lens
l = ((d2**2) - (d1**2)) / (4 * p * R)

#Result
print("Wavelength of light = %.f nm."%(l*1e9))

Wavelength of light = 2778 nm.


## Example 1.36, Page 1.53¶

In [146]:
from math import sqrt

# Given
l = 5.896e-7 # wavelength of light in meter
f = 1 # focal length of the plano-convex lens in meter
mu = 1.5 # refractive index of lens
n = 7 # no. of bright ring

#Calculations
p = 20 - 10
R = (f * (mu - 1)) * 2 # calculation for radius of lens
D = sqrt(4 * n * l * R) # calculation for diameter of 7th ring

#Result
print("Diameter of 7th bright ring = %.3e meter."%(D))

Diameter of 7th bright ring = 4.063e-03 meter.


## Example 1.37, Page 1.53¶

In [147]:
from math import sqrt

# Given That
lambda1 = 6e-7 # wavelength of first light in meter
lambda2 = 4.8e-7 # wavelength of second light in meter
r = 0.96 # radius of curvature of curved surface of lens in meter

#Calculations
n = lambda2 / (lambda1 - lambda2) # calculation for order of fringe
D = sqrt(4 * (n + 1) * lambda2 * r) # calculation for diameter of ring

#Result
print("Diameter of (n +1)th dark ring of lambda2. = %.2e meter."%D)

Diameter of (n +1)th dark ring of lambda2. = 3.04e-03 meter.


## Example 1.38, Page 1.54¶

In [148]:
from math import sqrt

# Given
lambda1 = 6e-7 # wavelength of first light in meter
lambda2 = 5.9e-7 # wavelength of second light in meter
r = 0.9 # radius of curvature of curved surface of lens in meter

#Calculations
n = lambda2 / (lambda1 - lambda2) # calculation for order of ring
D = sqrt(4 * (n + 1) * lambda1 * r) # calculation for diameter of ring

#Result
print("Diameter of nth dark ring of lambda1 = %.4f meter."%D)

Diameter of nth dark ring of lambda1 = 0.0114 meter.


## Example 1.39, Page 1.54¶

In [149]:
# Given
l = 5.896e-7 # wavelength of light in meter
D = 4e-3 # diameter of 7th brighter fringe in m
R = 1 # radius of curvature in m
n = 7 # for seventh brighter fringe

#Calculation
mu = 2*(2*n-1)*l*R / D**2 # calculation for refractive index of liquid

#Result
print("Refractive index of liquid = %.2f."%mu)

Refractive index of liquid = 0.96.


## Example 1.40, Page 1.54¶

In [150]:
# Given
D1 = 3e-3 # diameter of nth dark fringe when liquid is absent between the lens and the plate in m
D2 = 2.5e-3 # diameter of nth dark fringe when liquid is introduced between the lens and the plate in m
c = 3e8 # velocity of light in vacuum in m/sed

#Calculations
mu = D1**2 / D2**2# calculation for refractive index
v = 3e8 / mu # calculation for velocity of light

#Result
print("Refractive index of liquid = %.2f.\n velocity of light in the liquid = %.2e m/sec."%(mu,v))

Refractive index of liquid = 1.44.
velocity of light in the liquid = 2.08e+08 m/sec.


## Example 1.41, Page 1.55¶

In [170]:
# Given
l = 5.896e-7 # wavelength of light in meter
D = 5.1e-3 # diameter of 16th brighter fringe in m
R = 1 # radius of curvature in m
n = 16 # for sixteenth brighter fringe

#Calculation
mu = 4*n*l*R / D**2 # calculation for refractive index of liquid

#Result
print("Refractive index of liquid = %.2f"%mu)

Refractive index of liquid = 1.45


## Example 1.42, Page 1.55¶

In [171]:
from math import sqrt

# Given
l = 6.3e-7 # wavelength of light in meter
mu = 1.63 # refractive index of liquid
R = 0.9 # the radius of curvature of convex lens in meter

#Calculation
r = sqrt(l*R/mu) # calculation for the radius of smallest dark ring

#Result
print("The radius of smallest dark ring = %.2f mm."%(r*1000))

The radius of smallest dark ring = 0.59 mm.


## Example 1.43, Page 1.55¶

In [173]:
# Given
r = 10./7 # ratio of nth ring diameter for two media

#Calculation
R = (1/r)**2 # calculation for the ratio of refractive index of media

#Result
print("The ratio refractive index of media = %.f:100."%(R*100))

The ratio refractive index of media = 49:100.


## Example 1.44, Page 1.56¶

In [174]:
# Given
R = 0.9 # radius of curvature of the lower face of the lens in meter
D = 4.8e-3 # diameter of the 10th dark ring in meter
n = 10 # for 10th dark ring

#Calculation
l = D**2 / (4 * n * R) # calculation for wavelength of light

#Result
print("Wavelength of light = %.f A."%(l * 1e10))

Wavelength of light = 6400 A.


## Example 1.45, Page 1.56¶

In [175]:
# Given
r = 1./2 # ratio of 5th ring diameter

#Calculatio
R = (1/r)**2 # calculation for refractive index of liquid

#Result
print("Refractive index of liquid = %.f. "%R)

Refractive index of liquid = 4.


## Example 1.46, Page 1.56¶

In [177]:
from math import sqrt

# Given That
R = 1 # radius of curvature of lens of both side in meter
l = 5.4e-7 # wavelength of monochromatic light in meter
n1 = 5 # for 5th dark ring
n2 = 15 # for 10th dark ring

#Calculation
r1 = sqrt((n1*l)/(1/R + 1/R)) # calculation for radius of 5th dark ring
r2 = sqrt((n2*l)/(1/R + 1/R)) # calculation for radius of 15th dark ring
d = r2 - r1 # calculation for distance between 5th and 15th dark ring

#Result
print("Distance between 5th and 15th dark ring = %.3f cm."%(d * 100))

Distance between 5th and 15th dark ring = 0.085 cm.


## Example 1.47, Page 1.57¶

In [179]:
# Given
x = 2.5e-5 # distance moved by movable mirror in meter
t = 5e-5 # thickness of mica sheet in meter

#Calculation
mu = x / t + 1 # calculation for refractive index of mica

#Result
print("Refractive index of mica = %.1f"%mu)

Refractive index of mica = 1.5


## Example 1.48, Page 1.57¶

In [180]:
# Given
x = 6e-5 # distance moved by movable mirror in meter
N = 200 # no. of fringes crossed the field of view

#Calculation
l = (2 * x) / N # calculation for wavelength of light

#Result
print("Wavelength of light = %.f A."%(l * 1e10))

Wavelength of light = 6000 A.


## Example 1.49, Page 1.57¶

In [181]:
# Given
n = 50 # no. of bands crosses the line of observation
l = 5.896e-7 # wavelength of light in meter
mu = 1.4 # refractive index

#Calculation
t = n*l / (2*(mu-1)) # calculation for thickness of the plate

#Result
print("Thickness of the plate = %.2e m."%t)

Thickness of the plate = 3.69e-05 m.


## Example 1.50, Page 1.57¶

In [182]:
# Given
n = 50 # no. of bands crosses the line of observation
lambda1 = 5.896e-7 # max. wavelength of light in meter
lambda2 = 5.89e-7 # min. wavelength of light in meter

#Calculation
x = lambda1 * lambda2 /(lambda1 - lambda2) # calculation for the path difference

#Result
print("The path difference = %.4f mm."%(x*10**3))

The path difference = 0.5788 mm.


## Example 1.51, Page 1.58¶

In [183]:
# Given
x = 2.948e-5 # distance moved by movable mirror in meter
n = 100 # no. of fringes cross the field of view

#Calculation
l = 2*x/n # calculation for wavelength of monochromatic light

#Result
print("Wavelength of monochromatic light = %.f A."%(l * 1e10))

Wavelength of monochromatic light = 5896 A.


## Example 1.52, Page 1.58¶

In [184]:
# Given
lambda1 = 5.896e-7 # max. wavelength of light in meter
lambda2 = 5.89e-7 # min. wavelength of light in meter

#Calculation
x = lambda1 * lambda2 /(2*(lambda1 - lambda2)) # calculation for the path difference

#Result
print("The distance through which the movable mirror is move = %.3f mm."%(x*10**3))

The distance through which the movable mirror is move = 0.289 mm.


## Example 1.53, Page 1.58¶

In [185]:
# Given
x = 2.945e-4 # distance moved by movable mirror in meter
l = 5.893e-7 # mean wavelength of light in meter

#Calculation
delta_lambda = l**2 / (2*x) # calculation for difference between two wavelengths

#Result
print("Difference between two wavelengths = %.3f A."%(delta_lambda*1e10))

Difference between two wavelengths = 5.896 A.


## Example 1.54, Page 1.58¶

In [188]:
# Given
n = 140 # no. of shift in fringe
l = 5.46e-7 # wavelength of light in meter
t = 0.2 # length of tube in meter

#Calculation
mu = (n*l)/(2*t) + 1 # calculation for refractive index of gas

#Result
print("Refractive index of gas = %.5f"%mu)

Refractive index of gas = 1.00019