Lesson Plans Resolution Worksheet
Resolution Worksheet
I) Objective: Become familiar with units and calculations in resolution.
II) Intro:
1. Resolution can be described by the equation
(q) = 1.22 (l/d)
Where θ = resolution in
radians
d = diameter of dish or aperture
2. Angular distances of degrees can be subdivided
into 60 minutes of arc, with each minute of arc subdivided into 60 seconds of
arc so:
1
degree = 60 minutes of arc = 3600 degrees of arc
3. In order to calculate radians into arc seconds,
use the following:
Radian
= 2.06 X 105 arc seconds
4. Figuring out distances. Use appropriate units
Using geometry, we can figure out the distance of an
object, how big it is and the resolution needed to see the object.
This can be illustrated in the following illustration
and equation
N.B.
Drawing of angular size of object is exaggerated

Equation: Θ (in radians) = diameter of object/distance
This is true for small angle q
III)
Problems:
A. Basic conversion
1. How many arc seconds
in an angular size of 32 degrees?
2. How many radians in
6.3 X 106 seconds of arc?
3. The moon takes up 0.5
degrees of arc in the sky. How many
radians is this?
B. Resolution:
1. Using a telescope with an aperture diameter of 37
meters, you wish to observe a wavelength of 3 mm. What is the resolution of the telescope?
-Would you be able to resolve two objects with an
angular distance of 15 arc seconds?
2. Using the resolution you figured out in question
one, calculate the diameter of a telescope if you had to observe at 21 cm.
C. Distances
1. The moon is 384,000 km distant from the earth and
takes up an angular size of 0.5 degrees, what is the diameter of the moon?
2. How big (in angular size) is an object that has
an angular size of two arc seconds from a distance of 1000 km?
3. Using the size of object in question 2, how far
is the object if it takes up an angular size of 20 arc minutes?
D. Putting it all together
1.You have a 0.5-meter
telescope, and are looking at a blue object (~400nm).
a. What is
the resolution of your telescope
b. What is the maximum distance you could resolve the object, if the object has a diameter of 0.3 mm?