In a Young's double slit experiment, the separation between the two slits is `0.9 mm` and the fringes are observed one metre away. If it produces the second dark fringe at a distance of `1 mm` from the central fringe, the wavelength of the monochromatic source of light used is

Options

A. `450 nm`
B. `400nm`
C. `500nm`
D. `600nm`

Answer

D

Explanation

Fringe width is the separation between two consecutive dark or bright fringes. `rArr beta=(lambdaD)/(d)` From `C_(B)` to the second dark fringe, one covers 3/ 2 fringe width
`therefore`    `beta=1mmxx(2)/(3)`
  Thus, `(2xx1xx10^(-3))/(3)=beta=(lambdaxx1m)/(0.9xx10^(-3))`
`rArr`   `lambda=(2xx0.9xx10^(-6))/(3)=600mm`