what is the relation between wavelength and refractive index? is it U1 * A1 = U2 * A2 Un = refractive index An=wavelength in the medium n

u1a1=u1a1=u2a2=........   i.e ua=constant

yes ,you r right.

the purpose of studying about refractive index (u)  is to know whether the given medium is  rarer or denser . this(u) again represents whether speed of light is more or less in that medium. speed of  light is less in a denser medium(more u value).i.e., u and speed of light are inversely proportional .

but, speed, v = f n   ;

  u  =  k/ v

u  =  k / f n .

u n = k/f = constant. f= frequency of light = constant.

hence , u1 n1 = u2 n2