At sunset, red light travels horizontally through the doorway in the western wall of your beach cabin, and you observe the light on the eastern wall. assume that the light has a wavelength of 700 nm, that the door is 1.0 m wide, and that the distance from the door to the far wall of your cabin in 14 m .part adetermine the distance between the central bright fringe and a first-order dark fringe of the interference pattern created by the doorway "slit".

Explanation:

For light passing through a single slit, the position of the nth-minimum from the central bright fringe in the diffraction pattern is given by

where

is the wavelength

D is the distance of the screen from the slit

d is the width of the slit

In this problem, we have

is the wavelength of the red light

D = 14 m is the distance of the screen from the doorway

d = 1.0 m is the width of the doorway

Substituting n=1 into the equation, we find the distance between the central bright fringe and the first-order dark fringe (the first minimum):