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

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

Solution:

Fresnel’s distance (ZF) is the distance for which the ray optics is a good approximation. It is given by the relation,

$Z_{F}=\frac{a^{2}}{\lambda}$

Where,

Aperture width, a = 4 mm = 4 ×10−3 m

Wavelength of light, λ = 400 nm = 400 × 10−9 m

$Z_{F}=\frac{\left(4 \times 10^{-3}\right)^{2}}{400 \times 10^{-9}}=40 \mathrm{~m}$

Therefore, the distance for which the ray optics is a good approximation is 40 m.

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