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


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.