Question

Find the separation of two points on the Moon's surface that can just be resolved by a telescope with a mirror diameter of 6.5 m, assuming that this separation is determined by diffraction effects. The distance from Earth to the Moon is 3.82 x 105 km. Assume a wavelength of 550 nm. Number Units

Answer 1

To develop this problem it is necessary to apply the concepts related to the angular resolution of a telescope as well as to the arc length.

The arc length can be defined as

$s = r\theta$

Where

r= Radius

\theta = Angle

At the same time the angular resolution of a body is given under the proportion

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

Where

$\lambda$= Wavelength

D = Diameter

Our values are given as

$\lambda = 550*10^{-9}m$

$D = 6.5m$

$r = 3.82*10^5Km = 3.82*10^8m$

Then the angle of separation of the two objects seen from the observer is of

$\theta = 1.22 \frac{550*10^{-9}}{6.5}$

$\theta = 1.032*10^{-7}$

Finally, using the proportion of the arc length, in which we have the radius and angle we can know the separation of the two objects by:

$s = (3.82*10^8)(1.032*10^{-7})$

$s = 39.43m$