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Question
I don't understand where to start with this problem. I know it has something to do with diffraction. Thanks for any help.

Light with a wavelength of 600 nm passes through a double slit and an interference pattern is observed
on a screen 2.00 m from the slits. The first-order bright fringe is at 4.00 mm from the center of the
central bright fringe. For what wavelength will the first order dark fringe be observed at the same point
on the screen?

Answer
The first bright fring occurs when:
 n1*lambda1=d*x/L where n1=1 and lambda1=600nm
The first dark fringe occurs when:
n2*lambda2=d*x/L where n2=1/2 and lambda2 is the answer.
Using transitivity since both quantities and equal to the same d*x/L:
n2*lambda2=n1*lambda1
And solving for lambda2:
lambda2=(n1/n2)*lambda1=(1/1/2)*600=2*600=1200nm

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I am teaching or have taught AP physics B and C [calculus based mechanics & electricity and magnetism] as well as Lab Physics for college bound students. I have a BS in Physics from the University of Pittsburgh and a Master of Arts in Teaching from same. I have been teaching physics for 34 years. I am constantly updating my skills and have a particular interest in modern physics topics.

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