In Young's double slit experiment, 427 nm light gives a fourth-order bright fringe at a certain location on a flat screen. What is the longest wavelength of visible light that would produce a dark fringe at the same location

λ' = 379.22nm

Explanation:

In order to find the longest wavelength that allows one to dark fringe coincides with the bright fringe, you use the following formulas:

         (1)

      (2)

y-dark and y-bright are the positions of dark fringes and bright fringes respectively.

m: order of the fringe (dark or bright) = 4

D: distance to the screen

d: distance between slits

λ: light for y-bright= 427nm

λ': second light for y-dark = ?

By the information of the statement you know that y-bright = y-dark.

You divide equation (2) into the equation (1) and solve for λ':

 (3)

Finally, you solve the equation (3) by replacing the values of m and the wavelength:

The longest wavelength which produces the fourth dark fringe in the same location for the fourth bright fringe of the first wavelength is 379.22nm

resonant frequency