In a biprism experiment, the distance between the first and eleventh bright fringes formed by light of wavelength `lambda` is `1.8 xx 10^(-3)`m. If the light is replaced by one width wavelength `0.8 lambda`, find the distance between the first and sixteenth bright fringes.

Explanation

Data, `x_(11b)- x_(1b) = 1.8 xx 10^(-3)m,lambda_(1) = 0.8 lambda`
The distance of the nth bright fringe from the central bright fringe is
`x_(nb) = (nlambdaD)/d = nX`
`therefore` With light of wavelength `lambda`,
`x_(11)b - x_(1b) = 10X = 1.8 xx 10^(-3)`m
`therefore X= 1.8 xx 10^(-4)`m
Since the fringe width is directly proprotional to the wavelength, of light used, the fringe width with light of wavelength `lambda_(1)` is
`X_(1) = 0.8X = 1.44 xx 10^(-4)`m
Then, with light of wavelength `lambda_(1)`,
`x_(16b)-x_(1b)= 15X_(1) = 15(1.44 xx 10^(-4)) = 2.16 xx 10^(-3)`m