Graphical Inverse Relationship for single slit

[SaintJude]

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So in a single slit set up in which diffraction occurs. Kaplan says that as the "slit becomes narrower, the central maximum becomes winder."

Which graph accurately show the relationship? I don't have then answer.

The linear inverse

The curved inverse

I think it's the inverse curved graph b/c the the location of the dark fringes is given by the formula asinθ = nλ = constant.
And sinθ is directly proportional proportional to the width of the central maxima
So asinθ = constant are represented by the inverse curve graph. 👍👎?

 

[SaintJude]

bump.

 

[chiddler]

what are the axes?

meh nvm i don't know.

 

[milski]

That's correct, it will be inversely proportional. The distance from the center to the first minimum (dark spot) is L*tan θ, where L is the distance between the screen and the slit. From a sin θ = λ we have sin θ = λ/a and for small θ sin θ = tan θ. That means that the distance to the first dark spot is y=L*tan θ=L*sin θ=Lλ/a or a*y=Lλ=const.