Turn a resolution target into an illuminated width

Two nearby lines around 500 nm are separated by 0.10 nm. An ideal grating is used in first order and has 500 lines per millimetre.

What minimum illuminated width meets the ideal Rayleigh resolving-power requirement?

Organize the givens & assumptions

λ = 500 nm
Δλ = 0.10 nm
m = 1
Line density = 500 mm⁻¹

Uniform coherent illumination; ideal narrow slits, normal incidence, accessible unsuppressed order; use N = line density × illuminated width and neglect edge counting.

A $1.0\ \mathrm{mm}$
B $20.0\ \mathrm{mm}$
C $10.0\ \mathrm{mm}$
D $5.0\ \mathrm{mm}$

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