A ten centimeter (about 4 inches) reflecting telescope is used to look at the Mo
ID: 1314687 • Letter: A
Question
A ten centimeter (about 4 inches) reflecting telescope is used to look at the Moon. (each part is worth three questions)
a) What is the light-gathering power as compared to that of the human eye - assume that the pupil of the eye is 0.5 cm when fully dialated. How much greater is the amount of light gathered by the telescope (remember the formula for area)
b) Using 500 nanometer light (yellow-green) what is the smallest angular separation between two points that our telescope could resolve? (that'a alpha in the equation on p.132)
c) The Moon is 380,000 kilometers from the Earth. What is the smallest distance between two points that our telescope could distinquish (that is, what is the smallest object that could be seen from Earth using a 10 cm reflecting telescope?)
Use the information in the "Bringing it down to Earth" lecture, if you know the angular separation and you know the distance you know the physical separation between two ends of an object at that distance)
Explanation / Answer
A ten centimeter (about 4 inches) reflecting telescope is used to look at the Moon.
(each part is worth three questions)
a) What is the light-gathering power as compared to that of the human eye - assume that
the pupil of the eye is 0.5 cm when fully dialated. How much greater is the amount of
light gathered by the telescope (remember the formula for area)
The amount of light gathered is proportional to the area of the aperture, so the ratio of the
light gathering power of the telescope to the eye is
x = (? x 102/4) / (? x 0.52/4)
= 400
b) Using 500 nanometer light (yellow-green) what is the smallest angular separation
between two points that our telescope could resolve? (that'a alpha in the equation on
p.132)
The angular resolution is given by the Rayleigh criterion:
? =1.22 x ?/D =1.22 x 500 x 10-9/0.10
= 1.22(5
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