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 = a²/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.