Aberrations; a lecture in Optics. 4

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. More…

Two new Baryons at LHC. Reply

Two new Baryons at LHC.

Two new Baryons at LHCb.
LHCb, the famed experiment at CERN, Switzerland found a year ago two new Baryons. These are important steps in testing the validity of our state of the art understanding of current model of the Physical Universe, mostly in considering the “particle constituents” of the matter around us, and known by the name Standard Model — of Particle Physics.

Atoms with nuclei and electrons. Nucleus has nucleons in it which are two types, protons and neutrons. The protons and neutrons are Baryons with each having two different combination of 3 quarks — uud and udd.

Protons and Neutrons as Baryons, that is an eternal bond of 3 quarks. uud and udd. Note that the spring is the gluon. Much like a spring transmits a mechanical force these gluons have an assigned duty to transfer the strong nuclear forces from one participant to the other.

1. First off it does so by colliding protons with protons at gigantic speeds, at the speed of light. So these protons are 1000 times more energetic than their own mass. If you are 60 kg, your energy is 600 Joule, if you move freely a distance of 1 meter, consider yourself to be thrown so fast that you have 1000 times that energy. Both examples are approximately true.

2. Protons are called Baryons. Anything with 3 quarks in them, as we know them today are called as Baryon. The 3 quarks will never separate into single relationship status. Its a triangular love, in which each partner has their share of love meted out. Sorry particles are decidedly promiscuous. 😉 And never break their relations as long as they are bonded this way.

3. These new baryons — 3 quarks in eternal bonding, are about 6 times heavier than proton. SInce protons were bombarded onto each other madly, with energies that are 1000 times bigger than their own mass, the possibility of heavier particles such as these new baryons materialized. So the protons did not break in a way quarks will cry out “I am single again” but rather go into relationships with other quarks and form heavier relationships. More…

LIGO in India? You must be kidding … Reply

I was pleasantly surprised that this experiment is slated to come up in India, yes, with a whopping 250 million dollars investment into science in India is perhaps the only 2nd instance of massive science euphoria.

And they are both directly or immediately so, in my field of research, although the first one INO isn’t seeming to be coming of age, while collaborations and Physics and engineering as such have been extensively laid out in the ground, the lab the much coveted international particle physics lab that is, hasn’t come.

(Surprise me, if work has already begun in Madurai, we have been struck by paranoia of environment so much that the elephants have the right of way more than the most innocuous science commies out there, pardon me, that’s a pun, no disrespect to elephants, no offense to commies.) More…

Blackholes and the Action Principle. Reply

This is not an article that purports to establish any link between what I have to say about Blackholes and what I have to say about Action Principle.

First off there are always a connection between action principle and anything else in Physics. Everything in principle can be derived from the action principle. The action principle is the general principle of all sorts of mechanics in Physics and has the weird power of superiority over everything else, at-least in principle. So if you want to claim something is inconsistent in Physics, take a piece of chalk and chalk out how it is that the action principle is inconsistent with anything that you want to discard. The action principle has the key to proving how consistent or inconsistent Physics is.

And I am not stating the action principle much, either. I just wish to mention two ideas that have no explicit connection to be brought out by this article. Hence they are to be read without any purported conjunctions of one with the other. More…

Waves, particles and Einstein ! 1

Waves are something that have no mass and move at the maximum speed, mass m = 0. speed c = 1. So whats their momentum? p = m.v = 0? Right?

No. For pure waves; momentum does not come from mass. It comes only from motion.

(pure wave; they do not have mass)

For matter waves, on the other hand, momentum comes in two ways, mass as well as motion.

(impure, now they have mass)

Albert Einstein recognized this fact and derived his relation; $latex E = \sqrt {(pc)^2+(mc^2)^2}$

This relation is called as Einstein’s relativistic equation, also Einstein’s mass-energy relation. But more appropriately mass-energy-momentum relation.

Let us consider E as the hypotenuse, p and m; as base or perpendicular as is your choice.

triangle_copyThen $latex E = \sqrt {(pc)^2+(mc^2)^2}$ is Pythagoras Theorem; when p is momentum and m is mass.

For pure waves such as photon … the quanta of light, m = 0.

Hence the Pythagorean Triangle is now one, where the mass side is arbitrary small. Thus E = p. More…

What happens when cows move rapidly ! Reply

Cows not moving and moving fast. How does this difference impact the image in a modern digital camera?

Honestly I haven’t checked it with old day manual camera neither do I remember what impact motion brings into mages taken by such, eg does anyone remember when he/she took a picture of a friend standing in a platform and a train was coming, what happened to the image due to such motion?

Do you see where the fuzziness coming from, in the pictures, where the cows are moving?

Its coming from the relative motion between “objects being imaged” (cows and grass etc) and equipment of imaging (camera). This fuzziness is quite small when they are both still (the object and camera, wrt each other). More…