For what distance is ray optics a good approximation when the aperture is 3 mm wide and the wavelength is 500 nm?

18 m

The correct answer is Option (4) → 18 m

Ray optics is a good approximation when the Fresnel number is large or when diffraction effects are negligible. The condition is:

$ L \gg \frac{a^2}{\lambda} $

Here, aperture $a = 3 \text{ mm} = 3 \times 10^{-3} \text{ m}$, wavelength $ \lambda = 500 \text{ nm} = 5 \times 10^{-7} \text{ m}$.

$ \frac{a^2}{\lambda} = \frac{(3 \times 10^{-3})^2}{5 \times 10^{-7}} $

$ = \frac{9 \times 10^{-6}}{5 \times 10^{-7}} $

$ = 18 \text{ m} $

Therefore, ray optics is a good approximation for distances much greater than 18 m.