Double-slit experiment: wavelength for minimum at same location as blue light maximum

[Moxin]

In a double-slit experiment it is found that blue light of wavelength 478 nm gives a second-order maximum at a certain location on the screen. What wavelength of visible light would have a minimum at the same location?


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I have no clue how to approach this problem but looking in the book I assumed the wavelength with a minimum at that same location should be 3rd order (m=3) so I set up an equation as follows:


m1*Lambda(max) = m2*Lambda(min)
Lambda(min) = m1*Lambda(max)/m2 = (2*478*10^-9)/3 = 319 nm

Apparently it's wrong. I'm lost on where to go from here.. Any help ??

 

[quantumdude]

The minimum from the second wavelength needn't be of the same order. Also, you need to note that diffraction minima are not described by the same equation as diffraction maxima.

The minima are located by:

d*sin(θ)=(m+1/2)λ

You have d and θ. You also need to note that m must be an integer.

Can you take it from there?

 

[Moxin]

yeh i actually tried somethin like that before but i just now realized the other wavelength's m should be an order less (1, instead of 3) and i got it right, thanks tho !