Question

The Keck Telescope has a diameterof 10.0 m. When it is looking atMars, 7.38 1010 m from us, how farapart are the closest objects it couldpossibly resolve? Assume the lighthas wavelength 633 nm.[?] m

Answer 1

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):

`\theta=(1.22\lambda)/(D)`

Thus, we have:

Now, to find the distance of the closest objects, we have:

`d=\theta *x`

Thus, we have:

`\begin{gathered} d=7.7226*10^(-8)*7.38*10^(10) \\ \\ d=5699.28\text{ m} \end{gathered}`

Therefore, the distance of the closest objects is 5699.28 meters.

• ANSWER:

5699.28 m