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# Transmission Diffraction Grating

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A small transmission diffraction grating has width w = 0.25 mm and is composed of 16 narrow slits whose centers are spaced by 15um. It is situated in the z = 0 plane with its lines oriented along the y-direction, where the z-axis is defined to lie along the optical axis of a thin lens of focal length f = 2.5 mm and a diameter 2w positioned at z = 2f. The grating is parallel to the lens, but off-axis, extending from x = 0 to x = w/ The grating is uniformly illuminated by a parallel beam of monochromatic light of wavelength 750 nm propagating in the positive z-direction (the beam has width w and just fills the grating). Find the angle to the normal of the first-order diffracted beam as it leaves the grating, and draw a ray diagram showing rays leaving the edges of the grating in the zeroth and first-order diffraction directions and propagating through the lens to z = 10mm.

Sketch on the large diagram the light intensity distribution in the plane at z = 7.5 mm, indicating the locations of the principal maxima and the separations of these maxima from the first adjacent minimum. Sketch on a large diagram the light intensity at the plane z = 10mm.

Explain briefly how this example gives a useful insight into the resolving power of a microscope with coherent illumination.