Chapter 22 Diffraction and polarisation

Example 22.1 Page no 1124

In [4]:
#Given
D=1                           #m
l=5*10**-7                      #m
d=0.1*10**-3                    #m

#Calculation
W=(2*D*l)/d

#Result
print"Width of the central maximum is", W*10**2,"cm"

Width of the central maximum is 1.0 cm

Example 22.2 Page no 1124

In [13]:
#Given
D=1.60                          #m
l=6328*10**-10                        #m
w=4.0*10**-3

#Calculation
d=(2*D*l)/w

#Result
print"Width of the slit is", round(d*10**3,2),"mm"

Width of the slit is 0.51 mm

Example 22.3 Page no 1124

In [27]:
#Given
l=7500*10**-10
d=1.0*10**-6
c=20

#Calculation
import math
a=l/d
b=math.asin(a)*180/3.14
A=2*b
x=c*math.tan(a*3.14/180.0)
w=2*x

#Result
print"(i) Width of central maximum is", round(A,0),"Degree"
print"(ii) Width of central maximum is",round(w*10**2,0),"cm"

(i) Width of central maximum is 97.0 Degree
(ii) Width of central maximum is 52.0 cm

Example 22.4 Page no 1125

In [33]:
#Given
l=6.3*10**-7                      #m
a=3.6                             #Degree
n=10

#Calculation
import math
d=(n*l)/math.sin(a*3.14/180.0)

#Result
print"Slit width is", round(d*10**3,1),"mm"

Slit width is 0.1 mm

Example 22.5 Page no 1125

In [38]:
#Given
l=5500*10**-10
d=0.01

#Calculation
import math
a=l/d
b=math.asin(a)*180/3.14

#Result
print"Angular deflection is", round(b,4),"Degree"

Angular deflection is 0.0032 Degree

Example 22.6 Page no 1125

In [40]:
#Given
lr=660
d=3.0

#Calculation
l1=(2*lr)/d

#Result
print"The value of lambda is",l1

The value of lambda is 440.0

Example 22.7 Page no 1126

In [46]:
#Given
l1=5890*10**-10                    #m
l2=5896*10**-10
d=2.0*10**-6                          #m
D=2                                 #m

#Calculation
x=(3*D*(l2-l1))/(2*d)

#Result
print"Spacing between the first maxima of two sodium lines is",x*10**4,"*10**-4 m"

Spacing between the first maxima of two sodium lines is 9.0 *10**-4 m

Example 22.8 Page no 1126

In [48]:
#Given
d=3*10**-3                     #m
l=500*10**-9                   #m

#Calculation
Z=d**2/l

#Result
print"Distance is",Z,"m"

Distance is 18.0 m

Example 22.9 Page no 1126

In [51]:
#Given
d=2*10**-3                               #m
l=600*10**-9                             #m

#Calculation
Z=d**2/l

#Result
print"Distance is",round(Z,2),"m"

Distance is 6.67 m

Example 22.10 Page no 1126

In [53]:
#Given
d=2*10**-3                      #m
l=5000*10**-10

#Calculation
Z=d**2/l

#Result
print"Fresnel Distance is",Z,"m"

Fresnel Distance is 8.0 m

Example 22.11 Page no 1129

In [60]:
#Given
l=5.50*10**-7                      #m
D=5.1

#Calculation
a=(1.22*l)/D

#Result
print"Minimum angular separation is", round(a*10**7,1)*10**-7,"rad"

Minimum angular separation is 1.3e-07 rad

Example 22.12 Page no 1130

In [66]:
#Given
l=6*10**-7                      #m
D=0.6
l1=10**10                         #m
r=10.0**4*9.46*10**15                  #m

#Calculation
a=(1.22*l)/D
a1=l1/r

#Result
print round(a1*10**10,2)*10**-10,"rad"

1.06e-10 rad

Example 22.13 Page no 1130

In [70]:
#Given
l=6000*10**-8
D=254.0

#Calculation
a=(1.22*l)/D

#Result
print"Limt of resolution of a telescope is",round(a*10**7,1)*10**-7,"Radian"

Limt of resolution of a telescope is 2.9e-07 Radian

Example 22.14 Page no 1130

In [78]:
#Given
D=600.0                            #cm
l=5.5*10**-5                      #cm
d=3.8*10**10                      #cm

#Calculation
a=(1.22*l)/D
x=d*a

#Result
print"Separation of two points is", round(x,0),"cm"

Separation of two points is 4250.0 cm

Example 22.15 Page no 1130

In [80]:
#Given
d=10**-4                                 #cm
l=5.8*10**-5                             #cm

#Calculation
Na=l/(2.0*d)

#Result
print"Numerical aperature of a microscope is", Na

Numerical aperature of a microscope is 0.29

Example 22.16 Page no 1131

In [86]:
#Given
u=1
l=600*10**-9                     #,

#Calculation
import math
rp=(2*u*math.sin(30*3.14/180.0))/l

#Result
print"Resolving power of a microscope is", round(rp*10**-6,2),"*10**6"

Resolving power of a microscope is 1.67 *10**6

Example 22.17 Page no 1133

In [91]:
#Given
l1=15*10**-10                            #m
l=6563*10**-10
c=3*10**8                               #m/s

#Calculation
v=(c*l1)/l

#Result
print"Speed of star is", round(v*10**-5,2),"*10**5 m/s"

Speed of star is 6.86 *10**5 m/s

Example 22.18 Page no 1133

In [95]:
#Given
l1=0.032
l=100.0
c=3*10**8

#Calculation
v=-(l1*c)/l

#Result
print"Velocity of star is",v*10**-4,"*10**4 m/s"

Velocity of star is -9.6 *10**4 m/s

Example 22.21 Page no 1142

In [118]:
#Given
a=60                        #Degree
a1=90

import math
A=math.tan(a*3.14/180.0)
ap=a1-a

#Result
print"(i) Refractive index of the medium is", round(A,3)
print"(ii) The refracting angle is",ap,"degree"

(i) Refractive index of the medium is 1.73
(ii) The refracting angle is 30 degree

Example 22.22 Page no 1142

In [122]:
#Given
a=1.33

#Calculation
import math
ap=math.atan(a)*180/3.14

#Result
print"Angle of incidence is", round(ap,0),"Degree"

Angle of incidence is 53.0 Degree

Example 22.23 Page no 1142

In [127]:
#Given
u=1.33
a=90

#Calculation
import math
ap=math.atan(u)*180/3.14
A=a-ap

#Result
print"Angle between the sun and the horizon is", round(A,0),"Degree"

Angle between the sun and the horizon is 37.0 Degree

Example 22.24 Page no 1142

In [132]:
#Given
u=1.5

#Calculation
import math
ap=math.atan(u)*180/3.14
r=90-ap

#Result
print"Angle of refraction is", round(r,1),"Degree"

Angle of refraction is 33.7 Degree

Example 22.25 Page no 1143

In [135]:
#Given
a=30                          #Degree
I=3                            #A
I0=4.0
I1=1

#Calculation
a=I/I0
a1=I1/I0

#Result
print"(i) Fraction of maximum light transferred for 30 degree is", a
print"(ii) Fraction of maximum light transferred for 60 degree is", a1

(i) Fraction of maximum light transferred for 30 degree is 0.75
(ii) Fraction of maximum light transferred for 60 degree is 0.25

Example 22.26 Page no 1143

In [140]:
#Given
ap=60                     #Degree
u=3

#Calculation
import math
a=1/math.sqrt(u)
C=math.asin(a)*180/3.14

#Result
print"Critical angle for this medium is", round(C,2),"Degree"

Critical angle for this medium is 35.28 Degree