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## Homework Statement

One diffraction grating has 9600 lines uniformly spaced over a width of 3cm, it is illuminated by light from a mercury vapour discharge.

The other has 5000 lines/cm and is a 3.5cm grating, this one is used in the second order to resolve spectral lines close to 587.8002 nm spectral line of iron

part 1 to 2 concern first grating, part 3 to 5 concern 2nd grating

i) What is the expected dispersion, in the third order, in the vicinity of the intense green line whose wavelength = 546nm

ii) What is the resolving power of this grating in the 5th order?

For second grating

iii) For wavelengths > the iron line, whats the shortest wavelength you can distringuish from the iron line

iv) for wavelengths < the iron line, whats the longest you could distringuish?

v) What range of λ is indistinguishable from the iron line?

## Homework Equations

Dispersion = dθ/dλ = m/acos(θ) -> ? θ = mλ/d (not sure about this)

Resolving power = Nm = λ/Δλ

Δλ = λ/m = free spectral range

## The Attempt at a Solution

i) 9600/3 = 3200 lines per cm => 1/3200 is the seperation = d

θ = mλ/d = 3*546*10^-9 * 3200? Is that what they want?

ii) Would that just be 3200*5? = Nm?

iii) sinθ=mλ/d unsure, find where sinθ = 1? Very unsure to be honest

iv) unsure about iii

v) unsure about iii

I'm really sketchy on this part of the subject, and my notes have no examples and when I google I'm not sure what formulas I'm supposed to be using.