A ruled diffraction grating has 300 lines per millimetre (period )

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 ruled diffraction grating has 300 lines per millimetre (period Λ=3.33 μm\Lambda = 3.33\,\mu\mathrm{m}), each open groove being about 1 μm1\,\mu\mathrm{m} wide, and is illuminated at normal incidence by sodium light, λ=589 nm\lambda = 589\,\mathrm{nm}. ((a)) Estimate the Fresnel number of a single groove, treated as an isolated aperture of half-width a=0.5 μma = 0.5\,\mu\mathrm{m}, at a distance z=10 mmz = 10\,\mathrm{mm} behind the grating, and say whether the light leaving one groove is already in the Fraunhofer regime there. ((b)) Estimate the Talbot self-imaging distance zTz_T of the grating as a whole, and compare it with the 10 mm10\,\mathrm{mm} distance in part (a). Explain, in one or two sentences, why self-images still form at zTz_T although a single groove is already in its own Fraunhofer regime there.

Related theory

Browse the problem library