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(B) The ray optics approximation is valid up to the Fresnel distance $(z_f)$, which is defined as the distance at which the spreading of the beam due

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(B) The ray optics approximation is valid up to the Fresnel distance $(z_f)$, which is defined as the distance at which the spreading of the beam due to diffraction becomes comparable to the size of the aperture.It is given by the formula: $z_f = \frac{a^2}{\lambda}$.Given values: Fresnel distance $z_f = 5 \,m$, wavelength $\lambda = 800 \,nm = 800 	imes 10^{-9} \,m$.Rearranging the formula for slit width $a$: $a = \sqrt{z_f \cdot \lambda}$.Substituting the values: $a = \sqrt{5 	imes 800 	imes 10^{-9} \,m^2}$.$a = \sqrt{4000 	imes 10^{-9} \,m^2} = \sqrt{4 	imes 10^{-6} \,m^2}$.$a = 2 	imes 10^{-3} \,m = 2 \,mm$.

$A$ light beam of wavelength $800 \,nm$ passes through a single slit and is projected on a screen kept at $5 \,m$ away from the slit. What should be the slit width for the ray optics approximation to be valid (in $\,mm$)?

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