Two wavelengths, max/min at same angle

[cashmoney805]

1. The problem statement, all variables and given/known data
Light goes through two slits 40 mm apart. Does an angle exist at which light of wavelength 440nm has a maximum and light of wavelength 660nm has a minimum?


2. Relevant equations
dsin\theta=m\lambda1 = maximum
dsin\theta=(m+ 1/2)\lambda2 = minimum


3. The attempt at a solution
I solved for sin\theta in each case, so I got:

m\lambda1 = (m+ 1/2)\lambda2

\lambda1 = 660nm
\lambda=440 nm

Now I'm stuck. Both Ms do not have to be the same, right? So do I have to solve for one of the Ms and stick it into an equation I listed in part 2 above? If so, that's a crazy calculation. Thanks!

[Redbelly98]

Correct, the m's can be different. But they must both be integers.

Are the slits really 40 mm apart? That's pretty far for an optical double slit setup.

[cashmoney805]

They're actually 40 nm apart, sorry.

[Redbelly98]

Are you sure it's not 40 μm?

[cashmoney805]

ah yes you're right