Estimate the distance for which ray optics is good approximation for an aperture of 4 mm and wavelength 400 nm.


An aperture illuminated by beam of light sends diffracted light. The distance travelled by diffracted beam at which, width of spread of central maxima (zλ/a) equals the size of the aperture (a) is called the Fresnel distance(ZF). Beyond this distance, ray optics is good approximation for an optical measurement.


For a light wave of given wavelength, say λ, and an aperture of length ‘a’ length, Fresnel distance,


ZF = a2


a = size of aperture


λ = wavelength of light


Given,


a = 4 mm = 4 × 10-3 m


λ = 400 × 10-9 m


Thus, ZF = (4 × 10-3)2 / 400 × 10-9


= 40 m


For distance greater than 40 m, ray optics is valid.


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