can anyone explain in detail the basis on which antenna size is determined?

Question

i mean why are short dipoles used ?why should they be of length (lambda / 2)?

Answer 1

Because it allows efficient transfer of energy.

With a properly designed matching circuit and a low loss transmission line, antennas of almost any length can be used, but with the caution that you pay attention to the words "properly designed" and "low loss".

Answer 2

A dipole antenna is resonate at lambda/2 only in free space. A practical dipole used on planet Earth has to be shortened about 2 percent over theoretical because of dielectric slowing of the wave in air. The shortening can be even more pronounced if the end of the dipole can see coupling to a ground plane caused by the rod being of finite diameter. Most thin wire dipoles are about 5 percent short at resonance. Fat dipoles (cage) with end loading (top hat) can be significantly shortened, the extreme being a bi-conal shape factor.

Answer 3

You want the current distribution on the antenna to be such that (for instance on a dipole antenna) the current distribution falls to zero at the very ends, this makes the energy transfer more efficient.

remember when people who had Improper or broken antennas on their televisions would put foil balls on the end of them? This is called capacitive endloading and made the antennas look longer (electrically) thus increased their efficiency at picking up signals.