Aberrations; a lecture in Optics. 1

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…

cow and calf

The problem of eating beef. Reply

Is eating beef an act which is so morally repugnant that it can take lives? We wouldn’t imagine such with an ideally and intellectually sensitive human society. But we don’t, we live in communities which does not care so much about what it can infer as “other’s” ways. Lets not get ourselves embroiled, to believe that, thats a superfluous statement.

One would argue, we do care about others values and culture and others ways of looking at things and at a grosser level others comfort in riding a public transport, others availability and unavailability in attending to us for what we need them for.

But, I am talking about “others” as a mark of identification and not an immediately concocted response, to deal with a social situation.

At a deeper level, we often transgress, into interfering with others ways, simply because, we identify them as ‘others’. We deliberately create a ruckus, about ‘issues’, simply because, the issues do not affect us the way we perceive it affects others.

Its dishonesty and its violence. Read a short article here why I think “dishonesty is violence”.

We gang up on others and create false notions of vulnerability and mark others as adverse, simply because we have deep prejudices of defining our roles and identifications, as being markedly different, from what we confer onto those, that would not fit into such roles.

One of the determinant, in delving into making a demarcation of what constitutes ‘others’, is the idea of proving superiority. And its an age old problem, but more than that it prevails in today’s communities, in a way it would not let us make progress as humans. More…

Uncertainty Principle and Photography ! Reply

why a moving object becomes fuzzy when you take its picture. Speed bears an uncertainty with momentum (hence energy ) just like time with energy and position with momentum. But for photons which are always ultra-relativistic we should not talk about its positions. Due to speed (relative motion of objects such as your and moving while other body parts being still) energy and momentum are uncertain. Hence position becomes uncertain. (Do not confuse between position of photon vs position/location on your image although its connected to wave-function collapse BEFORE or AFTER the observation ? is the question you should be asking, BEFORE the observation no sense of photon’s position, but AFTER collapse we do see only a particular outcome in terms of fuzzy images.) More…

What is it like to be in an Ivy League. Just a musing. Reply

The other aspect is from my own experience, while you are highly qualified, you are perhaps no more pouring in as much as even you would like to pour in, in terms of real research. You or your employers don’t want you to go into controversies, because they drain you out of wit and the employer runs into razor sharp issues. The Ivy Leagues have the “requisite infrastructure” which is cutting edge in a way preconceived notion kind of way. It really does not open the actual researchers to the issues involved in fundamental thinking. And sooner or later we all the highly intellectual kind belong to a level where we see our wit’s end. It takes the highly competitive experience of figuring out what exactly the Ivy League want from you for you and them to be successful lest which they are subjected to competitive and often no so harmless scrutiny from even tiny rats. More…

Nature of photons. Reply

Also (without any direct theoretical connection, but correlation through reality of nature)
3. Photons are classical only in the sense that we perceive light only when photons are produced in large numbers. So large that the laws of the small do not incur large errors because they are in large numbers. Statistically the errors are well understood and eliminated. But when they are produced in very small numbers we can not deduce their laws a priori. [which is why Quantum Mechanics was discovered only in 1920s and not in Galileo’s time, In his time the macroscopic behavior were understood and microscopic laws can never be produced from the understanding of macro scope just like a particular individuals attribute can’t be found from a large number of individual’s group attribute] More…

Uncertainty Principle Again. Reply

2. The object can be a large object, eg say something whose picture you are taking. But as explained above its not the energy of the object (or momentum) which is directly coming into the problem. That would be an added degree of concern if the object is moving with certain velocity, a reason why pictures are blurred. Because motion of objects introduces additional energy-time-momentum-position variables and their corresponding uncertainties. For the argument of the above problem one can imagine the large sized object, lets say a bird, is standing still on a tree while its picture is being taken. In that case if the wavelength of the light [few 100 nano meters = 1/10th of a micrometer] is used (eg in a digital-camera) the corresponding accuracy of the light will be less than micrometers. You can take a very sharp picture of the bird, which is lets say 6 inch long. But when you zoom in to a large degree, the inaccuracies will show up. [in this case how to see a micrometer level image? Is a computer sufficient to show us the uncertain edges of the pixels?] If the wavelength (here visible light) is so small, evidently by de-Broglie relationship, momentum or energy of such light is very large. But its not as large to disturb the feelings of the bird. The bird doesn’t have a problem with visible light, and such energy does not disturb its position or energy or any thing so to say. So while Quantum Mechanics is valid, we are accustomed to say this is a classical mechanics situation. To say QM is invalid is incorrect. To say QM is understood to be valid is a knowledgeable position. More…