# Diffraction Grating?

1. Nov 16, 2008

### InSpiRatioNy

Diffraction Grating??? [URGENT]

1. The problem statement, all variables and given/known data
Consider two monochromatic sources of light, blue light of wavelength λb = 460 nm and red light of wavelength 670 nm. The red light is shun upon a diffraction grating of density, nr = 10,000 lines per cm. A diffraction grating with what line density (lines/cm) is required to have the 2nd maximum (m=2) of blue light coincide with the 1stmaximum (m=1) of red light?

2. Relevant equations
.....I don't really know.

3. The attempt at a solution
I really don't have a clue, i don't even know relavant equations!

2. Nov 16, 2008

### Hootenanny

Staff Emeritus
Re: Diffraction Grating??? [URGENT]

3. Nov 16, 2008

### n0_3sc

Re: Diffraction Grating??? [URGENT]

Standard diffraction grating formula:

$$a(sin\theta_i + sin\theta_m) = m\lambda$$
where,
$$a = \frac{1}{N}$$

theta_i and theta_m are incident and m'th diffracted angles respectively. (Though you don't need them).
Form two equations and solve for N.

I'll leave you to it. I'm off to bed

4. Nov 17, 2008

### InSpiRatioNy

Re: Diffraction Grating??? [URGENT]

I'm confused, what are theta then? And how should I fit all values of the red and blue light in this formula?

5. Nov 17, 2008

### n0_3sc

Re: Diffraction Grating??? [URGENT]

Don't overthink this question - it is simpler than you think.
You're told that m=2 for one wavelength must lie on m=1 for another wavelength. (Therefore theta_m will be the same for both wavelengths).
(Note also the incident angles are the same because you assume the sources are collinear).

Form 2 diffraction grating equations given the known variables. Solve for the missing N.

6. Nov 17, 2008

### InSpiRatioNy

Re: Diffraction Grating??? [URGENT]

I got 7282.6, if it's right....

7. Nov 17, 2008

### n0_3sc

Re: Diffraction Grating??? [URGENT]

lines/cm.
It's what I got too.

8. Nov 17, 2008

### InSpiRatioNy

Re: Diffraction Grating??? [URGENT]

Okay Thanks!