Question

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

Answer 1

Here's your answer mate

Answer 2

Explanation:

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Fresnel's distance( $\sf Z_f$ is the distance for which the ray optics is good approximation.

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$\textsf{it is given by,}$

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$\sf \longrightarrow\:Z_f\:=\: \dfrac{a^2}{\lambda}$

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Where,

Aperture width, a = 400mm = $\tt 4\times 10^{-3}m$

Wavelength of light, λ = 400nm = $\tt 400\times 10^{-9}m$

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$\sf \longrightarrow\:Z_f\:=\: \dfrac{(4\times 10^{-3})^2}{400\times 10^{-9}}$

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$\sf \longrightarrow\:Z_f\:=\: \dfrac{^4\cancel{16}\times 10^{-6}}{\cancel{400}_{25}\times 10^{-9}}$

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