Geometrical Optics
for
1st year Physics Honours Course
By Arnab Gangopadhyay
Light
The light, with which we see, is a small part of the
vast spectrum of electro magnetic field.
Interaction of light with matter divided
into three regimes.
l << a
l~a
l >> a
Geometrical Optics
Physical Optics
EM Wave theory
Rays of Light
The rays are defined as the wave normal
The light behaves as stream of energy
travelling along the rays which are directed
outwards from the source.
They obey the classical laws of reflection
and refraction.
Rays of Light
Fermat’s Principle
The path along which the disturbance
travels from one point to another point is
such that the time taken is at a stationary
value
Refracting index is defined by
m=c/v
The time taken by the light ray is given by
1
nili
t=

c i
Snell’s law from Fermat’s principle
The total optical path is
  nd
.  n.d
As this to be minimum,
d
0
dx
After some simple algebra, one can find
n.sin i  n'sin r
Geometrical Optics by Euclidean Geometry
Considerations
•Rays considered are paraxial rays.
•tanq = sinq=q can be used
•A co-linear relationship exists
between LHS and RHS
•Image is said to be conjugate to the object
and vice-versa
•Reflected ray is conjugate to the incident ray
Cardinal points
There are total six cardinal or important plains.
Principal plane: The planes at which transverse
magnification is 1
Nodal plane: The planes at which the angular
magnification is 1
Focal plane: The plane has its conjugate at
infinity
The Helmholtz Lagrange Equation
This equation is most fundamental equation
of geometrical optics
This relates r.i. , angular magnification and
transverse magnification between LHS and
RHS of the optical system
The Helmholtz Lagrange Equation
n.h.tanu=n′.h′.tanu′
Reference
1. Geometrical and physical optics by
R.S. Longhurst
2. Fundamentals of Optics by F.A.
Jenkins and H.E. White.
3. Optics by A.Ghatak