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Suppose an astronomical telescope is being designed to have an angular magnification of 34.0. If the focal length of the objective lens being used is 86.0 cm, find (a) the required focal length of the eyepiece and (b) the distance between the two lenses for a relaxed eye. Hint: For a relaxed eye, the image formed by the objective lens is at the focal point of the eyepiece.

a. 2.53 \mathrm{cm}

b. 2.53 \mathrm{cm}

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in this problem. We have an astronomical telescope with the angler magnification 34. So let's write that down the angle magnification. Mm. Which is also the ratio of the objective focal length to the eyepiece focal length it calls 34. All right, so now the focal length of the object is also given, so f o is given, which is 86 centimeter. From this information we have, we can for part A, we can easily find the focal length of the eyepiece. So for part A, what we can do is just trivia raised this equation here for the angler magnification. And we can re write f B because f o over mm. And the focal length F or was 86 centimeter and the magnification is 34. And from here we will get 2.53 centimeter. Okay, so list some pin to part B for part B. We want to find the distance between the two lenses of the telescope. All right, so when the telescope is adjusted for relaxed, I the image formed by the objective blends is at the focal length of the eyepiece. So what that means is actually the distance between the the distance between the objective lens and I piss is gonna be the sum of the focal length of the objective and the I piss. And we have both focal lengths. So what, we're gonna do it if we just add this up? The 1st 1 86 86 centimeter plus 2.53 centimeter. From here, we get a D a point 53 centimeter. So this is the distance between the two lances.

University of Wisconsin - Milwaukee