Angular Position of 1st Dark Fringe in Two-Slit Interference Pattern?

AI Thread Summary
To find the angular position of the first dark fringe in a two-slit interference pattern, the correct formula is dsin(theta) = (n + 1/2)λ, where n is the order of the dark fringe. Given a wavelength of 470 nm and slit separation of 0.2 mm, this equation allows for the calculation of theta. The small angle approximation can be applied if the angle is small enough, simplifying calculations using tan(theta) = y/L. The discussion clarifies the distinction between formulas for maxima and minima in interference patterns.
NelielSwann
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Homework Statement


A blue laser beam of wavelength 470nm (in air) is incident on two narrow slits separated by .2mm and produces an interference pattern on a screen located 2m away from the two slits.

Find the angular position (in degrees) of the 1st dark fringe. Can you use the small angle approximation?


Homework Equations


dsin(theta)=n(lambda)
tan(theta)= y/L



The Attempt at a Solution


I've searched all over for a formula to find the dark fringes, but all i can find is one for the light ones. the dsin(theta)=n(lambda) is used for the maxima. what formula do i use for the minima/dark fringes?
 
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For dark fringes use dsin(theta)=(n + 1/2 )(lambda)
 
For two-slit interference, the minima are halfway in between the maxima.
 
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