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Estimate the distance for which ray optics

Question:

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

Solution:

Fresnel's distance $\left(Z_{F}\right)$ is the distance which is used in ray optics for a good approximation. Following is the relation,

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

Where,

Aperture width, a = 4 mm = 4 × 10-3 m

Wavelength of light, $\lambda=400 \mathrm{~nm}=400 \times 10^{-9} \mathrm{~m}$

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

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

 

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