Chapter 2 Diffraction of light

Example 2.1 Page no 85

In [1]:
#Given
w=6*10**-7
a=12*10**-7

#Calculation
import math
A=math.asin(w/a)*180/3.14

#Result
print"Half angular width of central bright maxima is",round(A,0),"degree"

Half angular width of central bright maxima is 30.0 degree

Example 2.2 Page no 85

In [4]:
#Given
a =0.2*10**-3                      #m
D =2.0                                # n m
x=5*10**-3

#Calculation
w=(a*x)/D
w1=w*1*10**10

#Result
print"Wavelength of light is", w1,"A"

Wavelength of light is 5000.0 A

Example 2.3 Page no 85

In [9]:
#Given
f=100                      #cm
L=6000*10**-8
d=0.01

#Calculation
x=1.22*f*L/d

#Result
print"Separation is",x,"cm"

Separation is 0.732 cm

Example 2.4 Page no 86

In [6]:
#Given
w=6*10**-7                          #m
D=2
x=5.0*10**-3

#Calculation
a=(w*D)/x

#Result
print"Slit width is", a*10**4,"*10**-4 m"

Slit width is 2.4 *10**-4 m

Example 2.5 Page no 86

In [16]:
#Given
w=589*10**-9
D=1
a=0.1*10**-3

#Calculation
import math
A=math.asin(w/a)
A1=2*A
y=D*A1
y1=y*100

#Result
print"Angular width of central maxima is", round(A1,3),"radian"
print"Linear width of central maxima is",round(y1,3),"cm"

Angular width of central maxima is 0.012 radian
Linear width of central maxima is 1.178 cm

Example 2.6 Page no 86

In [16]:
#Given
a=22.0*10**-5
L=5500*10**-8
n=1
n1=2

#Calculation
import math
a1=L/a
A=math.asin(a1)*180/3.14
a2=math.asin(2*L/a)*180/3.14

#Result
print"Angular position of two minima is",round(A,2), "Degree and", round(a2,0),"Degree"

Angular position of two minima is 14.48 Degree and 30.0 Degree

Example 2.7 Page no 87

In [33]:
#Given
n=1
L=5890*10**-10
a=3*10**-4

#Calculation
import math
A=math.asin((L/a)*180/3.14)
A1=math.asin((3*L)/(2.0*a))*180/3.14

#Result
print"Angle is", round(A1*10**2,0),"Degree"

Angle is 17.0 Degree

Example 2.8 Page no 87

In [40]:
#Given
L=4890*10**-10
a=5*10**-3
f=0.4

#Calculation
x1=f*L/a
x2=3*L*f/(2*a)
x=x2-x1

#Result
print"Distance between first dark fringe and new bright fringe is", x,"m"

Distance between first dark fringe and new bright fringe is 1.956e-05 m

Example 2.9 Page no 88

In [41]:
#Given
L=5000*10**-8                #cm
a=5000.0

#Calculation
n=1/(L*a)

#Result
print"Highest order spectrum is",n

Highest order spectrum is 4.0

Example 2.10 Page no 88

In [42]:
#Given
c=1/5000.0
w1=5890*10**-8                         #cm
n =2

#Calculation
import math
theta = math.asin ((n*w1)/c)*180/3.14
w2 =5896*10** -8
theta1 = math.asin ((n*w2)/c)*180/3.14
a= theta1 - theta 
w =5893*10**-8
dw=w2 -w1
N=w/( dw*n)
N1= floor (N)

#Result
print"(a) Angular width is",round(theta,3),"Degree"
print"(b) Angular separation is",round(a,3),"Degree"
print"(c) No. of lines is",N1,"Grating"

(a) Angular width is 36.104 Degree
(b) Angular separation is 0.043 Degree
(c) No. of lines is 491.0 Grating

Example 2.11 Page no 89

In [28]:
#Given
w1=589*10**-9
w2 =5896*10**-10 
dw=w2-w1                               # change o f wave l eng th
w=( w1+w2) /2.0                       #mid wavelength
n =1

#Calculation
N=w/(n*dw)
N1= floor (N)

#Result
print"Number of lines is", N1,"grating"

Number of lines is 982.0 grating

Example 2.12 Page no 89

In [44]:
#Given
n1=2
n2=3.0
L=6360                        #A

#Calculation
L2=n1*L/n2

#Result
print"Wavelength is",L2,"A"

Wavelength is 4240.0 A

Example 2.13 Page no 89

In [48]:
#Given
L1=5400*10**-8
L2=4050.0*10**-8
a=30                        #Degree
b=1350.0*10**-8

#Calculation
A=b/(L1*L2*2)

#Result
print"Number of lines is", round(A,0)

Number of lines is 3086.0

Example 2.14 Page no 90

In [9]:
#Given
a=30                      #Degree
L=5000*10**-8
x=0.01                  #Radian

#Calculation
import math
A=math.tan(a*3.14/180.0)
X=1/A
L1=L*x*X

#Result
print"Difference in two wavelength is", round(L1*10**8,1),"A"

Difference in two wavelength is 86.7 A

Example 2.15 Page no 90

In [59]:
#Given
#Given
c=1/4000.0                        # grating element
w=5000*10**-8
n =3

#Calculation
import math
D=n/(c* math.sqrt (1 -((n*w/c)**2) ))

#Result
print"Dispersive power is",D*10**-4,"*10**4 rad/sec"

Dispersive power is 1.5 *10**4 rad/sec

Example 2.16 Page no 90

In [84]:
#Given
a=30                   #Degree
n=2.0
A=5000.0

#Calculation
import math
L=math.sin(a*3.14/180.0)/(n*A)

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

Wavelength is 4998.0 A

Example 2.17 Page no 91

In [5]:
#Given
l =5                            #length of grating
N =16000
w =6000
n =2.0

#Calculation
T=N*l
R=T*n
dw=w/(T*n)

#Result
print"(a) Resolving power is",R
print"(b) Wavelength is",dw,"A"

(a) Resolving power is 160000.0
(b) Wavelength is 0.0375 A

Example 2.18 Page no 91

In [94]:
#Given
w1=5500                         #A
w2=5501
n=2
W1=8500
W2=8501

#Calculation
w=(w1+w2)/2.0
W=w2-w1
N=w/W
W11=(W1+W2)/2.0
W12=W2-W1
N1=W11/W12

#Result
print"The required rosolving power", N1,"is less than the actual power"

The required rosolving power 8500.5 is less than the actual power

Example 2.19 Page no 92

In [87]:
#Given
c =12.5*10**-5
w=5*10**-5
N =40000

#Calculation
n=c/w
n1= floor (n)
P=n1*N

#Result
print"Resolving power is",P

Resolving power is 80000.0

Example 2.20 Page no 92

In [12]:
#Given
n=2500.0
w=0.5
n1=1
L=5890*10**-8
a=5000
L2=5896*10**-8
L3=5893*10**-8
c=6*10**-8

#Calculation
import math
A=w/n
A1=math.asin(L*a)*180/3.14
A2=math.asin(L2*a)*180/3.14
A3=A2-A1
N=L3/c

#Result
print"Angular separation between Two sodium lines are", round(A1,1),"degree and",round(A2,1),"degree"
print"Number of lines required is",round(N,0),"lines"

Angular separation between Two sodium lines are 17.1 degree and 17.2 degree
Number of lines required is 982.0 lines

Example 2.21 Page no 93

In [19]:
#Given
l=2               #inches
n=40000
N=3

#Calculation
r=n*l
p=N*r

#Result
print"The resolving power in third order is",p

The resolving power in third order is 240000

Example 2.22 Page no 93

In [35]:
#Given
N=40000.0
a=12.5*10**-5
w=80000

#Calculation
n=w/N
L=a/n
L1=L*10**8/(n*N)
L2=L*10**8+L1

#Result
print"Range of wavelength is", round(L2,2),"A"

Range of wavelength is 6250.08 A

Example 2.23 Page no 93

In [60]:
#Given
L=0.5*10**-8

#Calculation
import math
w=math.sin(10*3.14/180.0)*L/(math.cos(10*3.14/180.0)*(3/(60.0*60.0))*(math.pi/180.0))
W=w+L
N=W/(L*2)
N1=(N*2*w)/(L*2)

#Result
print"Minimum grating is", round(w*10**5,0)

Minimum grating is 6.0

Example 2.24 Page no 94

In [64]:
#Given
w=5000                            #A
N=30000
n=2.0

#Calculation
W=w/(n*N)

#Result
print"Smallest wavelength separation is", round(W,3),"A"

Smallest wavelength separation is 0.083 A

Example 2.25 Page no 95

In [11]:
#Given
f =50                        #focal length of convex lens in cm
w=5*10**-5                    #wavelength used in cm
n =1

#Calculation
import math
r= math.sqrt (n*f*w)

#Result
print"Radius is",r,"cm"

Radius is 0.05 cm

Example 2.26 Page no 95

In [12]:
#Given
d =0.2                       #diameter of ring
n =1
w=5*10**-5

#Calculation
r=d/2.0
f=(r**2) /(w*n)

#Result
print"Position of brightest spot is",f,"cm"

Position of brightest spot is 200.0 cm

Example 2.27 Page no 95

In [72]:
#Given
f =1                              #focal length in m
n =1
w =5893*10**-10
n1 =3
n2=5

#Calculation
r= math.sqrt (n*f*w)
r1= math.sqrt (n1*f*w)
r2= math.sqrt (n2*f*w)

#Result
print"Radius is",round(r*10**4,2),"*10**-4 m,",round(r1*10**3,3),"*10**-3 m,",round(r2*10**3,3),"*10**-3 m"

Radius is 7.68 *10**-4 m, 1.33 *10**-3 m, 1.717 *10**-3 m

Example 2.28 Page no 95

In [76]:
#Given
f1=8
w1=6000*10**-8
w2=4800.0*10**-8

#Calculation
f2=f1*w1/w2

#Result
print"Focal length is",f2,"cm"

Focal length is 10.0 cm

Example 2.29 Page no 95

In [78]:
#Given
n=1

#Calculation
f1=n

#Result
print"Principal focal length is",f1,"cm"

Principal focal length is 1 cm

Example 2.30 Page no 96

In [74]:
#Given
r =200                         #radius of curvature in cm

#Calculation
f=r

#Result
print"Principle focal length is",f*10**-2,"m"

Principle focal length is 2.0 m