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(\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 (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`