An EM wave from air enters a medium. The electric fields are
`overset(vec)E_(1)=E_(01)hatx cos[2piv((z)/(c )-t)]` in air and
`overset(vec)E=E_(02)hatx cos [k(2z-ct)]` in medium, where the wave number k and frequency v refer to their values in air. The medium is non-magnetic. If `in_(r_(1))` and `in_(r_(2))` refer to relative permittivities of air and medium respectively, which of the following options is correct ?

Options

A. `(in_(r_(1)))/(in_(r_(2)))=4`
B. `(in_(r_(1)))/(in_(r_(2)))=2`
C. `(in_(r_(1)))/(in_(r_(2)))=(1)/(4)`
D. `(in_(r_(1)))/(in_(r_(2)))=(1)/(2)`

Answer

C

Explanation

Velocity of EM wave is given by `v=(1)/(sqrt(mu in))`
`"Velocity in air"=(omega)/(k)=C`
`"Velocity in medium "=(C )/(2)`
Here, `mu_(1)=mu_(2)=1` as medium is non - magnetic
`therefore ((1)/(sqrt(in_(r_(1)))))/((1)/(sqrt(in_(r_(2)))))=(C )/(((C )/(2)))=2 rArr (in_(r_(1)))/(in_(r_(2)))=(1)/(4)`