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…
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.
A. What’s the speed of an electron in a cathode ray tube if the electric field and magnetic field are of unit strength in SI unit? Calculate magnetic force experienced by the electron. 4 marks
B. Derive the formula for magnetic field produced by an infinitely long straight conductor. 4 marks More…
(c) Fission of U – 235 nucleus releases 200 MeV of energy. Calculate the fission rate (i.e. no. of fissions per second) in order to produce a power of 320 MW.
(a) What’s the ratio of the shortest wavelength of Balmer series to the shortest wavelength of the Lyman series?
(b) What are the (i) energy (ii) magnitude of momentum, and (iii) wavelength of the photon associated with spectral emission of H-atom transition; n=3 state to n=1 state? More…
(vi). Write an equation of Lorentz force F acting on a charged particle having charge q moving in a magnetic field B with a velocity v in vector form.
(vii). What is the value of power factor in a series LCR circuit at resonance?
(viii). An a.c. generator generates an emf ‘e’ given by : e = 311 Sin (100 πt) volt. Find the rms value of the emf generated by the generator.
(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. More…