Question

Which power of a telescope might be expressed as "0.5 seconds of arc"?

A. resolving power.
B. the prism.
C. poor resolving power
D. magnifying power.

Answer 1

A) resolving power would be most appropriate

1 deg = 1/360 of circle

1 min = 1 deg / 60

.5 sec = 1/120 min

P(ower) = 1 deg / (60 * 120) = 1.4E-4 deg

Resolving power = .00014 deg

Objects separated by .00014 deg

In radians 1 deg = 360 / (2 * π) = 57.3 deg / rad

.00014 deg * 1 rad / 57.3 deg = 2.4E-6 rad

S = R θ separation where R is radius and θ in radians

If we let R = 250,000 distance to moon then

S = 250,000 * 2.4E-6 = .6 mi

.5 sec of arc could resolve objects .6 mi apart on moon