Two wavelengths, max/min at same angle

[cashmoney805]

Homework Statement

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?

Homework Equations

dsin$$\theta$$=m$$\lambda$$1 = maximum
dsin$$\theta$$=(m+ 1/2)$$\lambda$$2 = minimum

The Attempt at a Solution

I solved for sin$$\theta$$ in each case, so I got:

m$$\lambda$$1 = (m+ 1/2)$$\lambda$$2

$$\lambda$$1 = 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