Solve Diffraction Grating for Red & Blue Light [URGENT]

[InSpiRatioNy]

Diffraction Grating? [URGENT]

Homework Statement

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?

Homework Equations

...I don't really know.

The Attempt at a Solution

I really don't have a clue, i don't even know relavant equations!

Please help. THanks

 

[Hootenanny]

I really don't have a clue, i don't even know relavant equations!

Have you read your course text or class notes?

 

[n0_3sc]

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

 

[InSpiRatioNy]

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

 

[n0_3sc]

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.

 

[InSpiRatioNy]

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

 

[n0_3sc]

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

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

 

[InSpiRatioNy]

Okay Thanks!