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

Options

A. 12
B. 18
C. 24
D. 30

Answer

b

Explanation

In Young's double-slit experiment,
fringe width `= (lambda D)/(d)`
Given that
`x_(2) - x_(1) = 12 (lambda_(1) D)/(d)`
where `lambda_(1) = 600` nm. Also,
`x_(2) - x_(1) = k (lambda_(2) D)/(d)`
where `lambda_(2) = 400` nm and k is the number of fringes.
Dividing Eq. (i) by Eq. (ii),
`1 = (12 lambda_(1))/(k lambda_(2))`
`:. k = (12 xx 600)/(400) = 18`
Correct option is (b).
.