Advertisements

aberration

Primary Aberrations, 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.

Advertisements

Aberrations; a lecture in Optics.

Lecture-I; delivered 24-1-2017

This lecture has been delivered in one of the honors class 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:

Object point does not lie far away from the axis of the optical system.

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

The domain of optics where above two assumptions are valid is called as Paraxial optics. Paraxial systems are highly idealized and in reality 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 sin function by the Maclaurin series. 

If instead the 2nd term in the Maclaurin series retained and higher order terms are truncated then we say it’s a 3rd order theory — as opposed to the 1st order theory which we called the paraxial optical assumption. If a single wavelength source of light is considered along with a 3rd order theory the deviations from 1st order theory results thus obtained are summed up as primary or monochromatic aberrations. These aberrations are also known as Seidel aberrations in accordance with the name of the scientist Ludwig Von Seidel who studied them.

Thus these primary aberrations are broadly categorized into 5 types;

Spherical aberration
Coma
Astigmatism
Petzval field curvature
Distortion

The first 3 type of aberration lead to a deterioration in the quality of the image making them unclear. The last 2 types cause deforming of the shape or size of the images.

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

Enjoy this blog? Please spread the word :)

Skip to toolbar