Physics - Wave Optics Question with Solution | TestHub

The distance up to which ray optics is a good approximation is given by the Fresnel distance $Z_F$.

The formula for Fresnel distance is:

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

Given:

Aperture width, $a=6\text{ mm}=6\times 10^{-3}\text{ m}$

Wavelength, $\lambda =6000\text{ A˚}=6000\times 10^{-10}\text{ m}=6\times 10^{-7}\text{ m}$

Substituting the values into the formula:

$Z_F=\frac{(6\times 10^{-3}{)}^2}{6\times 10^{-7}}$

$Z_F=\frac{36\times 10^{-6}}{6\times 10^{-7}}$

$Z_F=6\times 10^1=60\text{ m}$

Thus, ray optics is valid up to a distance of $60\text{ m}$.

Answer: $60$ m