Single Slit Interference Pattern: Increased Distance

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Increasing the distance between the single slit and the screen results in wider bright fringes and decreased light intensity, making them appear closer together. This phenomenon occurs because the spreading of light reduces the distinction between dark fringes. The discussion raises questions about whether dark fringes actually decrease in size or if this is merely a perceptual effect. Key quantities relevant to this analysis include the wavelength of light and the distance from the slit to the screen. Understanding these factors is essential for accurately describing the interference pattern.
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Homework Statement
A laser emitting light with a wavelength of 560 nm is directed at a single slit, producing an interference pattern on a screen that is 3.0 m away. The central maximum is 5.0 cm wide.

What would the effect on this pattern be, if the screen was moved further away?
Relevant Equations
Δy = λL/w
ATTEMPT AT SOLUTION

The effect on the pattern when the screen is moved further away is the bright fringes would become wider, the light intensity of the bright fringes would decrease, and the bright fringes will appear closer together.

REASONING

I answered this question based on how light works against a screen in general. The part I get stuck on is how the dark fringes would appear. I state that the bright fringes "appear" closer together because as the distance between the slit and the screen increases the bright fringes would become wider, spreading the light outwards making the dark fringes harder to distinguish. Would the dark fringes actually get smaller or is it just a perception?
 

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What expressions do you know about where the bright and dark fringes appear? What quantities are relevant? Start from there.
 
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