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(Z _{F}). 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,

Z_{F} = a^{2}/λ

a = size of aperture

λ = wavelength of light

Given,

a = 4 mm = 4 × 10^{-3} m

λ = 400 × 10^{-9} m

Thus, Z_{F} = (4 × 10^{-3})^{2} / 400 × 10^{-9}

= 40 m

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

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