Respuesta :
Given:
Diameter, D = 10.0 m
Distance, x = 7.38 x 10¹⁰ m
Wavelength, λ = 633 nm
Let's find how far apart the closest objects it could possibly resolve.
First, apply the formula for the angle for angle separation (limit of resolution):
[tex]\theta=\frac{1.22\lambda}{D}[/tex]Thus, we have:
[tex]\begin{gathered} \theta=\frac{1.22*633\times10^{-9}}{10.0} \\ \\ \theta=\frac{7.7226\operatorname{\times}10^{-7}}{10.0} \\ \\ \theta=7.7226\operatorname{\times}10^{-8}\text{ rad} \end{gathered}[/tex]Now, to find the distance of the closest objects, we have:
[tex]d=\theta *x[/tex]Thus, we have:
[tex]\begin{gathered} d=7.7226\times10^{-8}*7.38\times10^{10} \\ \\ d=5699.28\text{ m} \end{gathered}[/tex]Therefore, the distance of the closest objects is 5699.28 meters.
• ANSWER:
5699.28 m
