Question

Class XII problem

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

Answer 1

 The distance for which ray optics is a good approximation is given by the Fresnel's distance.
aperture, a = 4 mm = 4×10^(-3) m
wavelength, $\lambda$ = 400nm = 400×10^(-9) m

$Z_F= \frac{a^2}{ \lambda} = \frac{(4 \times 10^{-3})^2}{400 \times 10^{-9}} =\frac{16 \times 10^{-6}}{4 \times 10^{-7}}=\boxed{40m}$