Solve Slit Grating Problem: Compute Wavelength of Light

[Xile]

1. With light from a gaseous discharge tube incident normally on a grating with slit separation 2.23 μm, sharp maxima for a certain wavelength of light are produced at angles θ = -17.1° and +17.1°. Compute the wavelength of the light in nanometers.



2. I thought this would work... (wavelength) = d * sin θ, but it turns out its a bit more complicated, i can't find anything in my books to describe a situation like this or how to solve it.

 

[merryjman]

I would think the equation you mentioned $$n \lambda = d sin\theta$$ would work. The only think I can think of is that the problem seems to imply that there is no central maximum, meaning that for $$\theta =0$$ the superimposed waves destrucively interfere. In that case, I think you use $$n(\lambda + 1/2) = d sin\theta$$ , but I'm not sure about that.

 

[yiuyan]

It seems to me that there are not enough information to solve the question. A maxima is formed from a double slit when the difference between the distance from each slit to a point is a multiple of the wavelength. If the light is coherent and basically the same, there should be a zeroth order maxima between the slits.