aberration

Primary aberration, a lecture in optics.

Lecture-II; delivered on 27-1-2017

In our Lecture-I  we discussed the phenomena of aberrations that arise because of a discrepancy of a first order theory and the 3rd order theory as depicted by the Maclaurin series; where we saw that first order theory represents the so called paraxial optical systems.

Please have a look of the linked article to get a basic view of the ground on which we are discussing this topic. At-least going half-way through the lecture and stopping short of the derivation will do well.

We discussed that there are two kind of aberrations. Monochromatic and Chromatic. As the name suggests the monochromatic aberrations are a result of the discrepancy when we considered our incoming ray to be having a single wavelength of light.

The chromatic rays on the other hand can have multiple colors or wavelength of light. The monochromatic aberrations are also called as Seidel or Primary aberrations and we will shed more light on them today.

The chromatic aberrations were dealt in greater detail — eg the derivations pertained to the chromatic aberrations. We did so because the chromatic aberrations are simple to understand.

So lets discuss in detail the 5 types of primary aberrations now.

Primary Aberrations.
1. Spherical Aberration.
When Paraxial Rays  refract after emerging from an object point they meet at a sharp focus.
But when non-paraxial or marginal rays emerge — or appear to emerge, from an axial object point they do not meet at a sharp focus.
Therefore different rays meet at different focal points. The resulting aberration is called as spherical aberration.

Aberrations, a lecture in optics.

Optics series Lecture — I
Optical Aberrations
delivered on 24 – 1 – 2017 — all optics series lectures can be accessed here. 

This lecture has been delivered in one of the honors class that I am teaching this semester. You will do really well to read the linked article on Optical path and Fermat’s principle which is not not intended as a honors lecture.

Optical systems are studied under two assumptions:

a. Object points do not lie far away from the axis of the optical system.

b. Rays taking part in image formation make a small angle with the axis of the optical system.

The domain of optics where the above two assumptions are valid is called as Paraxial optics. Paraxial systems are highly idealized and in reality they do not perfectly represent the situation. The consequential errors in image reconstruction are known as aberrations.

The paraxial assumption can be represented by truncating at the first term of the polynomial expansion of the sine function by the Maclaurin series.

I.S.C. Board Question Paper. Physics, Class XII – 2009 ( C.I.S.C.E. )

Question 1 
Answer all question briefly and to the point.

(i)
Explain the statement ‘relative permittivity of water is 81’.

(ii)
Draw (at least three) electric lines of force due to an electric dipole.

(iii)
Find the value of resistance X in the circuit below so that the junction M and N are at the same potential.

(ix)
A ray LM of monochromatic light incident normally on one refracting surface AB of a regular glass prism ABC emerges in air from the adjacent surface AC as shown in Figure. Calculate the refractive index of the material of the prism.

SECTION A
(Answer any two questions)

Question 2 
(a)
With the help of a labeled diagram, obtain an expression for the electric field intensity ‘E’ at a point P in broad side position (i.e. equatorial plane) of an electric dipole.

Question 3
(c)
(i) State any two differences between a moving coil galvanometer and a tangent galvanometer.

(ii) What is the use of a Cyclotron?

SECTION C
(Answer any two questions)

Question 8
(a)
Electrons, initially at rest, are passed through a potential difference of 2 kV. Calculate their:

(i) Final velocity and

(ii) de Broglie wavelength