In a double-slit experiment, two parallel slits are illuminated first bylight of wavelength 400 nm and then by light of unknown wavelength. The fourth-order dark fringe resulting from the known wavelength of light falls in the same place on the screen as the second-order bright fringe from the unknown wavelength. The value of unknown wavelength of light is

Options

A. 900 nm
B. 700 nm
C. 300 nm
D. none of these

Answer

b

Explanation

`y_(n) = (n + (1)/(2)) (D lambda)/(d) , n = 1, 2, 3`
`(3 + (1)/(2)) (D lambda_(1))/(d) = 2 xx (D lambda_(2))/(d)`
`lambda_(2) = (7)/(4) xx 400 = 700` nm