Determine the change in wavelength of light during its passage from air to glass. Refractive Index of Glass with respect to Air is 1.5 and the frequen
Determine the change in wavelength of light during its passage from air to glass. Refractive Index of Glass with respect to Air is 1.5 and the frequency of light is ` 5 xx 10 ^( 14 ) ` Hz. Also find the wave number of light in glass (velocity of light in air ` c = 3xx 10 ^( 8 ) m//s ` ).
1 Answers
Given ` : mu _ g = 1.5, c = 3 xx 10 ^( 8 ) m//s, n = 5 xx 10 ^( 14 ) ` Hz
we know that, ` c = n lamda _ a `
` therefore lamda _ a = ( c ) / ( n ) = ( 3xx 10 ^( 8)) /( 5 xx 10 ^( 14)) = 6000 ` Å
` mu _ g = ( c ) /( v _ g ) = ( n lamda _ a ) /( n lamda _ g ) `
` therefore lamda _ g = ( lamda _ a ) /( mu _ g ) = ( 6000 ) /( 1.5 ) = 4000 ` Å
` therefore lamda _ a - lamda _ g = 6000 - 4000 = 2000 Å `
Wave number in glass,
` bar ( lamda _ g ) = ( 1 ) / ( lamda _ g ) `
` therefore bar (lamda _ g ) = ( 1 ) /( 4 xx 10^( - 7 ) ) = 2.5 xx 10 ^( 6 ) ` per m.