Question

Light from the air enters a transparent material which has an index of refraction of 2.0, which means that light travels half as fast in the material as it does in the air. How do the wavelength and the frequency of the light in the material compare to the wavelength and the frequency of the light in air?

Answer 1

Frequency of a wave is characterized by the source of wave so it will not change when a ray goes from one medium to another .

When light enters from air to a transparent material the refractive index of transparent medium is given by ,

$\mu =v_a/v_m$ , ...........................eq1

where $v_a=$ velocity of light in air ,

$v_m=$ velocity of light in transparent medium ,

we know $v=f\lambda$ ,

therefore eq1 becomes ,

$\mu =f{\lambda }_a/f{\lambda }_m$ ,

$2={\lambda }_a/{\lambda }_m$ ,

${\lambda }_m={\lambda }_a/2$