Why the velocity of light in vacuum is independent of wave length ?

Speed of any wave does not depend on the wavelength. It depends only on the elastic and inertia properties of the medium.

In vaccum if frequency increases wavelenth decreases, if wavelenth increases frequency decreases so velacity in vaccum is independent of wavelenth

n_a= refractive index of air   = 1

n_b=refractive index of vacume = 0

v_a=velocity of light in air  =3*10^8m/s

v_b=velocity of light in vacume

we know that n_a/n_b= v_b/v_a

then v_{b =} 3*10^8m/s

f_a  =  v_a/lmdab  ;  fb  =  vb_/lmdab

by this fa=fb&va=vb

then lmda a=lmada b

so that the velocity of light  in vacuum is independent of  wave length