Double Slit: Find Longest Wavelength

AI Thread Summary
To calculate the longest wavelength of light for a first-order maximum in a double-slit experiment with slits 1200nm apart, the relevant formula is sin(theta) = m(wavelength)/d. The discussion highlights confusion regarding the angle theta, as it cannot exceed ±90 degrees, which complicates the calculation. The book states the longest wavelength is 12nm, but participants question this, suggesting it may be incorrect due to a possible oversight in the calculation. The consensus is that the maximum wavelength should be slightly less than the slit separation, indicating a need to re-evaluate the provided answer. Overall, the conversation revolves around clarifying the correct application of the formula and the implications of the angle in determining wavelength.
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Question: Calculate the longest wavelength of light falling on double slits separated by 1200nm for which there is a first-order maximum. In what part of the spectrum is the light?

Answer in Book: 12nm

my problem: the formula i thought you would use is sin(theta) = m(wavelength)/d?? However you do not know an angle? any ideas??
 
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Of course -\frac{\pi}{2} < \theta < \frac{\pi}{2}. Can you solve it now?
 
yeah i get what that means and that theta could not be greater then 90 or less then -90, so then how do i incorperate that into the equation? and get 12 nm?:confused:
 
Plugging theta in would give

\lambda _{max} \approx d

Which according to your book is wrong. I'm stunned. I suppose the answer in the book is wrong: they've forgotten the zeros.
 
so the biggest possible wavelength that could be created would be slightly under the width between the two slits?? and thanks a lot for your help:smile:
 
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