# Chapter 7 Thin Lens, Coaxial Systems and Aberrations¶

## Example 7.1 Page no 114¶

In :
#given
f1=-12.0                                                        #Focal length of a converging lens in cm
f2=25.0                                                         #Focal length of a diverging lens in cm
d=8                                                           #Distance between the lens in cm

#Calculations
C=(1/f1)+(1/f2)+(d/(f1*f2))
D=(d/f2)+1
A=(d/f1)+1
O1F1=(-D/C)
O2F2=(A/C)
O1H1=(1-D)/C
O2H2=(A-1)/C

#Output
print"Position of cardinal points are O1F1 = ",round(O1F1,3),"cm, O2F2 = ",round(O2F2,3),"cm, O1H1 = ",round(O1H1,3),"cm, O2H2 = ",round(O2H2,3),"cm"
print"The system is in air, therfore, nodal points coincide with unit points"

Position of cardinal points are O1F1 =  18.857 cm, O2F2 =  -4.762 cm, O1H1 =  4.571 cm, O2H2 =  9.524 cm
The system is in air, therfore, nodal points coincide with unit points


## Example 7.2 Page no 115¶

In :
#given
f=15.0                                 #Focal length of achromatic doublet made up of crown and flint glasses in cm
fl=(0.01506,0.02427)                 #Dispersive power of crown and flint glasses respectively

#Calculations
#Solving two equations
#(1/f)=(1/f1)+(1/f2)
#(f1/f2)=(-0.01506/0.02427)
fx=(fl/fl)
f2=(-(1/fx)+1)/(1/f)
f1=(-fx*f2)

#Output
print"Focal length of converging lens is ",round(f2,1),"cm"
print"Focal length of diverging lens is ",round(f1,1),"cm"

Focal length of converging lens is  -9.2 cm
Focal length of diverging lens is  5.7 cm


## Example 7.3 Page no 115¶

In :
#given
f=20.0                                                  #Focal length in cm
fl=(0.015,0.019)                                        #Dispersive powers of crown and flint glasses respectively
r=(1.495,1.53)                                          #Refractive indices respectively

#Calculations
fx=-(fl/fl)
#Solving two equations
#(1/f)=(1/f1)+(1/f2)
#(f1/f2)=(-0.015/0.019)
f2=((1/fx)+1)/(1.0/f)
f1=(fx*f2)
r2=(r-1)*f2
r1=1/(((1/f1)/(r-1))+(1/r2))

#Output
print"Radius of curvature of converging lens is ",round(r2,1),"cm"
print"Radius of curvature of diverging lens is ",round(r1,1),"cm"

Radius of curvature of converging lens is  -2.8 cm
Radius of curvature of diverging lens is  7.9 cm


## Example 7.4 Page no 116¶

In :
#given
r=1.5                                                       #Refractive index of the material of a thin lens
f=-20.0                                                     #Focal length of the lens in cm
rx=-6.0                                                     #Ratio of radii of curvature of lens

#Calculations
r1=1/((1/f)/((r-1)*(1-(1/rx))))
r2=(rx*r1)

#Output
print"Radii of curvature of lens are ",round(r1,2),"cm and",r2,"cm"

Radii of curvature of lens are  -11.67 cm and 70.0 cm