Need help with width of slit (wavelength)

Question

anonymous · Answer

Light at two different wavelengths ( $$\lambda $$ = 750nm and wavelength $$\lambda $$= 450 nm) is shone through the same single slit at the same time. The two diffraction patterns are lined up to have a common central bright fringe, which appears on the screen 1.50 m from the slit. The shortest distance from the centre to where dark fringes from each pattern overlap is 6.75 cm. Determine the slit's width.

anonymous · Answer

@kropot72 Hey could you help me with this?

anonymous · Answer

$$\sin \theta = m \frac{ \lambda }{ W }$$ So I'd use this for dark fringes right? Then let this = bright fringes on single slit, but I'm having a hard time figuring out single slit with bright fringes.

vincent-lyon.fr · Answer

What you have to do is to find a pair of integers m1 an m2 so that m1λ1 = m2λ2, then solve for W.

anonymous · Answer

So m1 and m2 can be anything that will give you a wavelength between 450 and 750?

anonymous · Answer

I'm not exactly sure how to go on and do this, so I'd let m1 and m2 = 1 and then m1 = m2, then I can solve with the given variables?

vincent-lyon.fr · Answer

You need to find the least common multiple of 450 and 750.

anonymous · Answer

Oh wait, so just divide 450/750 right?

anonymous · Answer

m1/m2 = y2/y1 = 450/750 = 0.6

Is this right? Than I can find the angle and than eventually find W?