A circular iris of radius in a spectrometer is illuminated on-axis by light of wavelength

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Interference and diffraction · Interference and diffraction

What an Instrument Can See, Ch Scalar diffraction theory, derived

Problem

A circular iris of radius a=1.0 mma = 1.0\,\mathrm{mm} in a spectrometer is illuminated on-axis by light of wavelength λ=500 nm\lambda = 500\,\mathrm{nm}. A detector on the axis is placed a distance z=0.40 mz = 0.40\,\mathrm{m} beyond the iris; with the iris removed, the on-axis irradiance there would be I0I_0. ((a)) Compute the Fresnel number NFN_F and the (integer) number of Fresnel zones open within the iris. ((b)) Hence state whether the centre of the pattern is bright or dark, and give the on-axis irradiance in terms of I0I_0.

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