Estimate the distance for which ray optics is good approximation for an aperture of 4 mm and wavelength 400 nm.
Exercise
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Fresnel's distance $(Z_F)$ is the distance for which the ray optics is a good approximation. It is given by the relation,
$\text{Z}_\text{F}=\frac{\text{a}^2}{\lambda}$
Where,
Aperture width, $\mathrm{a}=4 \mathrm{~mm}=4 \times 10^{-3} \mathrm{~m}$
Wavelength of light, $\lambda=400 \mathrm{~nm}=400 \times 10^{-9} \mathrm{~m}$
$\text{Z}_\text{F}=\frac{\big(4\times10^{-3}\big)^2}{400\times10^{-9}}=40\text{m}$
Therefore, the distance for which the ray optics is a good approximation is 40 m.
$\text{Z}_\text{F}=\frac{\text{a}^2}{\lambda}$
Where,
Aperture width, $\mathrm{a}=4 \mathrm{~mm}=4 \times 10^{-3} \mathrm{~m}$
Wavelength of light, $\lambda=400 \mathrm{~nm}=400 \times 10^{-9} \mathrm{~m}$
$\text{Z}_\text{F}=\frac{\big(4\times10^{-3}\big)^2}{400\times10^{-9}}=40\text{m}$
Therefore, the distance for which the ray optics is a good approximation is 40 m.
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