A wide beam of laser light with a wavelength of 632.8nm is directedthrough sever

Question

A wide beam of laser light with a wavelength of 632.8nm is directedthrough several narrow parallel slits, separated by 1.20mm, andfalls on a sheet of photographic film 1.40 m away. Theexposure time is chosen so that the film stays unexposed everywhereexcept at the central region of each bright fringe. (a) Find thedistance between these interference maxima. The film isprinted as a transparency- it is opaque everywhere except at theexposed lines. Next, the same beam of laser light is directedthrough the transparency and allowed to fall on a screen 1.40mbeyond. (b) Argue that several narrow parallel bright regions,separated by 1.20mm, will appear on the screen, as real images ofthe original slits. If at last the screen is removed, lightwill diverge from the images of the original slits with the samereconstructed wave fronts as the original slits produced.(Suggestion: You may find it useful to draw diagrams similar toFigure 38.16. A train of thought like this, at a soccer game, ledDennis Gabor to the invention of holography.)

Explanation / Answer

given laser light wave length = =632.8*10-9m slit separated distance = d = 1.20mm =1.20*10-3m the several narrow parallel slits make a dirationgrating the zeroth and first order maxium are separate accordingto dsin = n where n = 1 then sin = /d = sin-1 (/d) plug in values = 0.000527rad    y = Ltan= 1.40m (0.000527) = 0.738mm B) many equally spaced transferent lines appear on thefilm it itself acting a diffraction grating when the same light sent through the film it produces interference maxiumseparated accordingto dsin = 1 sin = /d =632.8*10-9m/0.738*10-3m   =0.000857 y = Ltan = 1.40m (0.000857) = 1.20mm

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