In Young's double-slit experiment, the slit are 0.5 mm apart and the interference is observed on a screen at a distance of 100 cm from the slits, It is found that the ninth bright fringe is at a distance of 7.5 mm from the second dark fringe from the center of the fringe pattern. The wavelength of the light used in nm is

Options

A. `5000 Å`
B. `(5000)/(7) Å`
C. `2500 Å`
D. `(2500)/(7) Å`

Answer

a

Explanation

`y_(9) =` Position of 9th bright fringe `= 9 ((lambda D)/(d))`
`y_(2) =` Position of 2nd dark fringe `= (2 - (1)/(2)) (lambda D)/(d) = (3)/(2) (lambdaD)/(d)`
`y_(9) - y_(2) = 7.5 mm implies (lambda D)/(d) (9 - (3)/(2)) = 7.5 xx 10^(-3)`
`:. lambda = (7.5 xx 10^(-3)) ((2)/(5)) ((0.5 xx 10^(-3))/(100 xx 10^(-2)))`
`= (75) ((2)/(15)) (5) (10^(-4 -4)) = 50 xx 10^(-8) m`
`= 5000 Å`