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

Explanation

Wavelength of incident monochromatic light ,
`lamda =589 nm=589xx10^(-9)` m
Speed fo light in air ,`C=3xx10^(8) m//s`
Refractive index of water ,`mu =1.33 `
(a) the ray will reffect back in the same medium as that of incident ray , hence , the wavelength , speed and frrequency of the refiect ray will be the same as that of the incident ray .
Frequency of light is given by the relation ,
` V=(c) /(lamda) `
`=(3xx10^(8))/(589xx10^(-9))`
`=5.09 xx10^(14)` Hz
Hence the speed frequency and wavelength of the refliegth of the reflected light are `3xx10^(8)` m/s `5xx10^(14)` Hz and 589 nm respecticely .
(b) FRequency of light does not sepend on the property of the medium in which it is Travelling Hence the freqency of the refreative index of water as :
`V=(c)/(mu)`
`V=(3xx10^(8))/(1.33) = 2.26 xx10^(8) `m/s
Wavelength of light in water is given by the relation ,
`lamda =(V)/(V)`
`=(2.26 xx10^(8))/(5.09xx10^(14))`
`=444.007 xx10^(-9)`m
=444.01 nm
Hence th speed freuency and wavelength of refracted light are `2.26xx10^(8)` m/s 444.01 nm and `5.09 xx10^(14)` Hz respectively .