The twin paradox is fun to think about over a glass of warm milk. the idea is that one twin (jan, the active one) is an astronaut, while her sister (jen) observes the trip at home from the stocker astroscience center. [maybe jen "just likes to watch"] jan travels to alpha centauri (a distance of 4.22 light years), spends 1.00 year there taking measurements, and travels back to earth (again, a distance of 4.22 lightyears) and the spaceship has a velocity of v 0.9c (as measured in the frame of jen. obviously, the spaceship has no velocity as measured in the frame of jan). a) how far away does each sister see the distance between earth and alpha centauri? b) how long would jan measure for the time of the entire trip? c) how long would jen measure for the time of the entire trip? d) the texts like to talk about proper time. which frame here is the proper time? e) initially, since jan and jen are twins, they are the same age. which sister is now older? each sister thinks that in her frame, she sat still which is the paradox. f how do you fix that paradox?

a electromagnetic waves

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach

k2s for potassium sulphide