Monochromatic light of wavelength 589 nm is incident from air on a water surface. What are the wavelength, frequency and speed of (a) reflected, and (b) refracted light ? Refractive index of water is 1.33.

Explanation

Given , wavelength `lambda = 589 mm = 589 xx 10^(-9) m`
Speed of light in vacuum , `c = 3 xx 10^8 m//s`
(a) For reflected light : Wavelength and speed are same as that for the incident light. Therefore, frequency is
`v = c/lambda = (3 xx 10^8)/(589 xx 10^(-9))`
`= 5.093 xx 10^(14) Hz`
(b) For refracted light : Frequency remains same as that for the incident light.
`:. v = 5.093 xx 10^(14) Hz`
Speed of refraced light will be
`upsilon = c/(mu) = (3 xx 10^8)/(1.33) = 2.256 xx 10^(8) ms^(-1)`
Wavelength of refracted light will be
`lambda = (upsilon)/(mu) = (2.26 xx 10^8)/(5.09 xx 10^(14)) = 443 nm` .