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 Geometrical Optics

l ~ a Physical Optics

l >> a EM Wave theory

Rays of LightThe 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

t =1

i ii

n lc

Snell’s law from Fermat’s principle

. .n d n d

0d

dx

.sin 'sinn i n r

The total optical path is

As this to be minimum,

After some simple algebra, one can find

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

n.h.tanu=n′.h′.tanu′

The Helmholtz Lagrange Equation

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

Thank You For

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