All of Physics is this “Inherent ability = difficulty * accomplishment”. Thats just intuitive but can easily be seen to correspond mathematically with the Principle of least action.
First the edifice: whats the problem? The problem is given you move in straight line when every direction is same around you, which direction will you chose? While you are waiting for a good answer from astrologers intelligent people already give a good hint. Think you have some inherent ability which is fixed.
fixed: which changes only if estimated wrong.
That inherent ability is actually action. Accomplishments are adjusted for difficulties, you waded through a swamp 5 meters you would have accomplished in sand 8 meters with that given inherent ability called action. Because action is abstract we have been sticking to time and path-length, but they are not as fundamental, they are merely specifics. More…
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…
Finally I am successful in calculating pi value — less than 0.3% error, by using random number generation. Although my computer needs some fixation on its compiler or path definition etc, there are very good online compilers which helps in testing and running c++ codes: try the given link.
Computing the value of pi using std::rand()
Enter number of trials: 10000
Enter number of random (x,y) points per trial: 10
pi = 3.14376 +- 0.00519107
average – exact = 0.00216735
CPU time = 0.004027 secs
Here is the code I found by searching a good deal on the web. Yes I did tinker around but only because my own compiler (Turbo C++ on windows 10, 64 bits) was throwing some exceptions on the included headers.
using namespace std;
double pi_estimate(const unsigned long points) More…
The beauty of Maxwell’s equations can be seen in how it helps us understand nature as well as instruments, at the same time. Medical devices are simply an advanced understanding that began with understanding electromagnetic waves through Maxwell’s equations.
Each of the following 4 equations has a different name, by which we call’em, but together they are called as the Maxwell’s equations. Together they constitute what I am inspired to say; the golden equations of Physics. If we do some easy tricks they will be converted into whats called as the Wave Equations (of motion) ! Yes, they describe the wave behavior “fully”.
— By that I don’t mean sound waves, but any sort of waves that move at the speed of light. Sound waves are ordinary pressure oscillations, that travel much slower than even rockets.
The 4 equations therefore describe how electromagnetic waves are created and broadcast. Hence TV radio and satellite communication were understood because these 4 equations were understood.
First two are time-independent or static equations.
The first equation is known as Gauss’s law of electrostatics and says “Electric fields (E), are a result of sources of electrostatic charge”.
The 2nd equation is analogous and called as Gauss’s law of static magnetic field. But it says “apparently there are no sources of magneto-static charge or single magnetic pole from which the magnetic field B is created”.
Then how are magnetic fields created? We needed to know further to find the answer. Lets look at the 3rd and 4th equations. More…
A long and technical discourse on Quantum Wave Function.
A 64 slide presentation styled discourse on the Quantum Wave Function. It consists of detailed solution of 5 important and interesting problems, apart from a threadbare discussion of the concepts.
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…