Question

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

Answer 1

Given,
wavelength, $\lambda$ = 400nm = 4 × 20^-7m
aperture, $a$ = 4mm = 4 × 10^-3m

we know from Fresnel's concept ,
distance for which day optics is good approximation = Fresnel's distance $Z_F$

$\implies Z_F=\frac{a^2}{\lambda}$

= (4 × 10^-3)²/(4 × 10^-7)
= 40m

hence, distance for which ray optics is good approximation = 40m

Answer 2

Given :

Aperture =a= 4mm= 4x 10⁻³m

Wavelength =λ=400nm=400x 10⁻⁹ m

Ray optics is good approximation upto a distance equal to Fersnel's Distance[Zf]

Zf= a²/λ

=4x 10⁻³ x 4x 10⁻³/400x 10⁻⁹

Zf=40m

∴Estimated distance is 40m