Double Slit: Find Longest Wavelength

[SwAnK]

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??

 

[Päällikkö]

Of course $$-\frac{\pi}{2} < \theta < \frac{\pi}{2}$$. Can you solve it now?

 

[SwAnK]

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?

 

[Päällikkö]

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.

 

[SwAnK]

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