The telescope at a small observatory has objective and eyepiece focal lengths of
ID: 1285400 • Letter: T
Question
The telescope at a small observatory has objective and eyepiece focal lengths of 16.2 m and 12 cm, respectively. If this telescope is used to view a 1580 m diameter lunar crater on the surface of the Moon 3.77 108 m from the surface of the Earth, determine the following.
The telescope at a small observatory has objective and eyepiece focal lengths of 16.2 m and 12 cm, respectively. If this telescope is used to view a 1580 m diameter lunar crater on the surface of the Moon 3.77 times 108 m from the surface of the Earth, determine the following.angular magnification of the telescope (Include the appropriate positive or negative sign.size of the first image (Include the appropriate positive or negative sign.length of the barrel of the telescope.angle subtended at the unaided eye by the lunar crater.the absolute value of the angle subtended at the eye when the lunar crater is viewed through the telescope Draw a figure showing both lenses of the telescope, the object (lunar crater), the image formed by the objective, and the image formed by the eyepiece. See if you can determine how the angle subtended at the eye when the object is viewed through the telescope is related to the size of the image formed by the objective and the focal length of the eyepiece.Explanation / Answer
We know for telescope, magnification is
M = Fo/Fe = B/A
where
B = angle subtended by final image at eye
A is angle subtended by object at eye
M = 16.2/12 = 1.35
For objective lens Hi/Ho = V/U = 4.21*10-10
or Hi which is inverted = 1580 * 4.21*10-10 = 6.65 * 10-7 m
tanA = Hi/V = 6.65 * 10-7/ 0.162 = 41*10-8
or A = 4.1 * 10-6 radians
B/A = 1.35
or B = 5.54*10-6 rad
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