An electromagnetic wave has a wavelength ₀ in vacuum. It enters a material medium of relative permittivity _r and relative permeability _r . The wavelength of the wave in this medium will be:

Step-by-step solution

When an electromagnetic wave travels from one medium to another, its frequency ( f ) remains constant. The speed of the wave in vacuum is c = f ₀ , and in the medium it is v = f . Therefore, the wavelength in the medium is directly proportional to the wave speed: = ₀ ( v c ) The speed of light in a medium is given by v = c _r _r . Substituting this into the wavelength equation yields: = ₀ ( 1 _r _r ) = ₀ _r _r Answer: ₀ _r _r