An electromagnetic wave of frequency 3.0 MHz passes from vacuum into a non-magnetic medium with permittivity, `in =16 in_(0)`. Where `in_(0)` is the free space permittivity. The change in wavelength is

Options

A. `-75` m
B. `+75` m
C. `-50` m
D. `+50` m

Answer

A

Explanation

Given, frequency of EM wave,
`f=3 MHz`
`=3xx10^(6) Hz`
and permittivity of non-magnetic medium.
`epsi=16 epsi_(0)`
Wavelength of EM wave,
`lambda =c/f=(3xx10^(8))/(3xx10^(6))`
`lambda =100` m
Velocity of electromagnetic (EM) into non-magnetic material,
`v=c/sqrt(epsi_(r))=(3xx10^(8))/sqrt(16)" "[ :'epsi_(r)=epsi/epsi_(0)=16]`
`=3/4 xx10^(8)` m/s
`:.` Wavelength, `lambda'=v/f=(3/4xx10^(8))/(3xx10^(6))=25 m`
`:.` Change in wavelength `=lambda '-lambda`
`=25-100=-75 m`