In a Young's double slit experiment, 12 fringes are observed to be formed in a certain segment of the screen when light of wavelength 600nm is used. If the wavelength of light is changed to 400nm, number of fringes observed in the same segment of the screen is given by

Options

A. 18
B. 24
C. 30
D. 36

Answer

A

Explanation

If on a certain segment of the screen, `n_(1)` fringes of wavelength `lambda_(1)` are present and `n_(2)` fringes of wavelength `lambda_(2)` are present, then
`n_(1) beta_(1) = n_(2) beta_(2)`
`implies n_(1) (lambda_(1)D)/(d) = n_(2) (lambda_(2)D)/(d)`
`implies n_(1) lambda_(1) = n_(2) lambda_(2)`
`:. n_(2) = (n_(1) lambda_(1))/(lambda_(2)) = (12 xx 600)/(400) = 18`