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

the pull of gravity on the rocket decreases

that would be because of both gravity and friction. so     c