Question

The telescope at a small observatory has objective and eyepiece focal lengths respectively of 19.8 m and 12 cm. If this telescope is used to view a 1480 m diameter lunar crater on the surface of the moon 3.77 108 m from the surface of the Earth, determine the following. (a) angular magnification of the telescope -165 Your answer is correct. (b) size of the first image -7.8e-5m Your answer is correct. (c) length of the barrel of the telescope 19.92m Your answer is correct. m (d) angle subtended at the unaided eye by the lunar crater 3.9e-6 rad Your answer is correct. (e) angle subtended at the eye when the lunar crater is viewed through the telescope Incorrect: Your answer is incorrect. 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? I just need help with part e. Other answers are correct. Thank you.

Answer 1

M = angle subtended by image at eye (tan beta)/angle subtended by object at unaided eye (tan alpha) and M = focal length of objective (fo)/focal length of eye piece (fe) equating above two Hence tan beta/tan alpha = fo/fe tan beta/tan (3.9 times 10^-6) = 19.8/0.12 tan beta = 6.435 times 10^-4 beta = 6.4349 times 10^-4 rad