Answer:
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