Question

Consider two objects on the Moon's surface that can just be resolved by one of the 10.0 m telescopes at the Keck Observatory. What is the separation of the two objects? Assume the resolving power is only limited by diffraction effects. The distance from the Earth to the Moon is 3.8 x 105km, assume the wavelength of the light is 550 nm.

Answer 1

Answer: 25 m

Explanation:

The resolving power of a telescope is given by:

$\theta = 1.22\frac{\lambda}{diameter}$

Diameter of the telescope = 10.0 m

Wavelength of the telescope = 550 nm = 550 ×10⁻⁹m

Thus, the resolving power of one of telescopes at the Keck Observatory is:

$\theta = 1.22 \frac{550\times 10^{-9}}{10.0} =671 \times 10^{-10} rad = 3.85 \times 10^{-6} deg$

Also, $tan\theta = \frac {\text {separation between two objects}}{\text{distance to the objects}}$

separation between objects = tan (3.85×10⁻⁶)° × 3.8×10⁵km = 2.5 × 10⁻²km =25 m