Question

The Moon is one of the few astronomical objects that the unaided eye can see in any detail. 3. Estimate the angular resolution limit of the human eye at 550 nm. Take the diameter of the a. pupil to be 4 mm. b. How does this compare with the angular resolution limit of a 20 cm amateur telescope, observing at the same wavelength? What is the minimum size of a crater on the Moon that can be resolved in each case? (Take c. the distance to the Moon to be 3.844 x 105 km.) d. Are these resolution limits likely achieved? Why or why not?

Answer 1

Solution

a)

Angular resolution by Rayleigh criterion is

Ꮎ = 1.224

where, @ is the angular resolution

Lambda is the wavelength

D is the dia of pupils

Putting their values from the question

550nm 0 = 1.22 * 4mm

A = 0.0001678rad

b)

for telescope of D= 20cm

A = 0,000003355rad

c)

Resolving power is the smallest separation that the lens can see two different objects.

R= OL

Reyes = 0.0001678 * 3.844 * 10 km = 6.45km

Rtelescope = 0.000003355 * 3.844 * 10 km = 1.29km

d)

No, it is not likely achieved due to distortion in the atmosphere and diffraction due to the lens used. Some cases if objects are near behind high mass concentration due to gravity distortion might occur.