Solving Dark Fringes Problem with 651nm Light & 5.47x10^-6m Slit

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The discussion focuses on calculating the number of dark fringes produced by 651nm light passing through a single slit of width 5.47 x 10^-6 m. The formula sin(θ) = m × λ/Width is used to determine the order of the dark fringes. The user calculates the angle for m=1 as 6.83 degrees and seeks confirmation on the maximum value of m. They conclude that the maximum m, based on sin(θ) not exceeding 1, is 8, suggesting there will be 8 dark fringes on either side of the central maximum. The conversation emphasizes the relationship between the slit width, wavelength, and the resulting fringe pattern.
NotaPhysicsMan
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Hey, another question I'm working on.

How many dark fringes will be produced on either side of the central maximum if light, (651nm) is incident on a single slit that is 5.47 x 10^-m wide?

Ok, I figure I could use this forumula sin@= m x lambda/Width. Am I trying to locate the maximum m (the order of the dark fringe) that it'll go?

I tried solving for m=1 and got a angle of 6.83 degrees. Now where to?
Any tips/hints welcome.

Thanks.
 
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What do you know about the range of values of sin@ ?
 
I missed something, the W is suppose to be 5.47x10^-6 m. Well, I know it can't go past 90 degrees and the min is the central max, which is 0 degrees.
 
So if I put sin90=m x lambda/W and solve for m, then I'll get 8.40? so 8 dark fringes?
 
can someone verify please and thanks
 

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