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The wavelenght of light from sodium sourcein vacuum is 5893Å. What are its (a) wavelenght, (b) speed and ( c) frequency when this light travels in water which has a refractive index of 1.33. |
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Answer» Solution :Therefractive index of VACUUM, `n_(1) = 1` The wavelenght in vaccum, `lambda_(1) = 5893 Å` The speed in vacuum, `c = 3 XX 10^(8) ms^(-1)` The refractive index of water`n_(2) = 1.33` The wavelenght of light in water, `lambda_(2)` The speedof light in water, `v_(2)` (a) Theequation relating the wavelenght and refractive index is, `(lambda_(1))/(lambda_(2)) = (n_(2))/(n_(1))` Rewriting, `lambda_(2) = (n_(1))/(n_(2)) xx lambda_(1)` Substituting thevalues, `lambda_(2) = (1)/(1.33) xx 5893 Å = 4431Å RARR lambda_(2) = 4431Å` (b) The equation relating the speed and refractive index is, `(v_(1))/(v_(2)) = (n_(1))/(n_(2))` Rewriting, `v_(2) = (n_(1))/(n_(2)) xx v_(1)` Substituting the values, `v_(2) = (1)/(1.33) xx 3 xx 10^(8) = 2.256 xx 10^(8)` `v_(2) = 2.256 xx 10^(8) ms^(-1)` ( c)Frequency of light in vacuum is, `v_(1) = (c )/(lambda_(1))` Substituting the values, `v_(1) = (3 xx 10^(8))/(5893 xx 10^(-10)) = 5.091 xx 10^(14) Hz` Frequency of light in water is, `v_(2) = (v)/(lambda_(2))` Substituting the values, `v_(2)=(2.256xxx10^(8)ms^(-1))/(4431xx10^(-10))=5.091xx10^(14)Hz` The results shown that the frequency REMAINS smae in all media. |
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