Looking at diffraction gratings .

[qazxsw11111]

Looking at diffraction gratings...

Ok, so I got a question in my assignment.

Monochromatic light of wavelength l is incident normally on a diffraction grating consisting of alternate opaque strips of width a and transparent strips of width b. The angle between the emerging zero order and second order spectra is given by?

So I assumed that the slit separation is given by a since transparent strips (i assumed) is like those empty slits and slit separation is opaque.

So I tried dsinθ=nλ. But my ans is sin^-1 2l/a.
But the answer given is sin^-1 2l / (a+b)

Is there a problem in my understanding of the question?

EDIT: Is it because slit separation is calculated from the centre of each slit. Thus, the two 1/2 b will add together to get b, leading to slit separation a+b?

 

[tiny-tim]

Hi qazxsw11111!

EDIT: Is it because slit separation is calculated from the centre of each slit. Thus, the two 1/2 b will add together to get b, leading to slit separation a+b?

Yup! ​

 

[nlightner]

Yes, your understanding of the question is incorrect. The slit separation in this case is not just a, but rather a+b since it includes both the opaque and transparent strips. This is because the diffraction gratings consist of alternate opaque and transparent strips, so the overall slit separation is the sum of both widths. Therefore, the correct formula to use would be dsinθ=nλ, where d is the slit separation of a+b. This would give you the correct answer of sin^-1 2l/(a+b).