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

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Homework Help Overview

The discussion revolves around determining the number of dark fringes produced by a single slit diffraction pattern when illuminated by light of wavelength 651 nm and a slit width of 5.47 x 10^-6 m.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply a formula related to the sine of the angle for dark fringes and questions how to find the maximum order of the dark fringe. Other participants inquire about the range of values for sine and the implications of the angle being limited to 90 degrees.

Discussion Status

Participants are exploring the calculations and implications of the formula, with some verifying the values derived for the order of dark fringes. There is engagement in checking assumptions and clarifying the setup, but no consensus has been reached regarding the final count of dark fringes.

Contextual Notes

There is a correction regarding the slit width, and participants are considering the physical constraints of the problem, such as the maximum angle for sine and the implications for the number of dark fringes.

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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