Two-Slit Interference Question

[mneox]

Homework Statement

Suppose I have two different visible lights of different wavelengths passing through in a two-slit interference experiment. What appears on the screen is mostly a mixture of the two colours. However, one of the bright fringes, say m=2 is purely 1 of the colours (this light has say, 300 micrometers in wavelength), and none of the other.

What are the possible wavelengths of the second visible light?

Homework Equations

y = (R)(m)(lambda)/(d)
dsin(theta) = m(lambda)

The Attempt at a Solution

How do I figure this out? If none of the second colour appeared, it would mean that somehow there was interference and therefore only the first colour showed? How would I find the wavelengths of the second colour though.

Sorry I can't really give a better attempt or answer, I'm just so lost on this that it's discouraging. Thanks for your help/explanations in advance.

 

[sagardip]

See, for a mixture of colours to appear, both the colours can never undergo destructive interference as in that case there would be zero intensity(ideally) at the point where it happens.Now a bright fringe will have one color only if the light ray having the other color undergoes destructive interference at that point. So now you can apply the condition for destructive interference of the light of second wavelength and find it out.But of course before that you will have to find the distance of the point from the central maximum by using the values given for the light of 300 micro meter wavelength