In a four-slit experiment the distance between the central bright fringe and the second off-center bright fringe is 8 cm. What is the distance between adjacent dark fringes?

y' = 2 cm

Explanation:

In the system with more than two slits we can consider them a network and diffraction, which is described by the expression

d sin θ = m λ

Where d is the separation between the slits, λ the wavelength and m an integer that is the order of diffraction.

Let's use trigonometry for line separation

tan θ = y / L

Where L is the distance to the observation screen, in diffraction and measured angle experiments it is small

tan θ = sin θ / cos θ = sin θ

We replace

d y / L = m λ

This is the equation for constructive interference, it indicates that y = 8 cm for m = 2

d 8 / L = 2 λ

d / Lλ = 2/8

For the case destructive interference we must increase the length is wave is λ/2, the equation remains

d y' / L = (m + ½) λ

In the case of adjacent strips m = 0

d y' / L = (0 + 1/2) λ

d / Lλ = 1 / 2y'

Let's match the two diffraction equations

¼ = 1 / 2y'

2y' = 4

y' = 2 cm