Question

The telescope at Yerkes Observatory in Wisconsin has an objective whose focal length is 19.4 m. Its eyepiece has a focal length of 10.0 cm. (a) What is the angular magnification of the telescope? (b) If the telescope is used to look at a lunar crater (diameter = 5130 m), what is the size of the first image, assuming the surface of the moon is 3.77 × 108 m from the surface of the earth? (c) How close does the crater appear to be when seen through the telescope?

Answer 1

Part A) Here f_o [focal lenth of objective lense] = 19.4 m

f_e [focal lenth of eyepiece] = 10. cm = 0.1 m

Now Angular magnification (m ) = angle substenged by image ()/  angle subtended by image() = - f_o / f_e

   SO m = - 19.4 / 0.1 = 194

Part b) Here Diameter of Lunar Crator = 5130 m , DIstance of if from earth surface = 3.77 * 10 ⁸ m.

First Angle subtended by the Lunar crartor () = Daimeter of Lunar C. / Distance = 5130 / 3.77 * 10 ⁸

So     = 13.60 * 10 ^{6 .}

Now size of Image = f_o * = 19.4 * 13.60 * 10 ^{6 .} =2.64 * 10⁸