A terrestrial telescope has three lenses: an objective, an erecting lens, and an

Question

A terrestrial telescope has three lenses: an objective, an erecting lens, and an eyepiece. (a) Does the erecting lens (1) increase the magnification, (2) increase the physical length of the telescope, (3) decrease the magnification, or (4) decrease the physical length of the telescope? Explain. (b) The three lenses of this terrestrial telescope have focal lengths of 40 cm, 20 cm, and 15 cm for the objective, erecting lens, and eyepiece, respectively. What is the magnification of the telescope for an object at infinity? (c) What is the length of the telescope barrel?

Explanation / Answer

(a ) The object is at infinity. Assume that the object is erect. The objective forms a real and inverted image. For this object the eyepiece forms a final vitual inverted image. When we introduce an erecting lens between them this lens simply inverts the image without magnifying it. Hence the erecting lens increases the length of the telescope option (2). The length of the telescope increases by 4f (f = focal length of the erecting lens).

fo = 40 cm fe = 15 cm f = 20 cm D = 25 cm

(b) magnification m = fo/fe = 2.67(when the final image is at infinity)

when the final image is at near point m = (fo/fe) (1+ (fe/D)) = 4.27

(c) length of the telescope L = fo + 4f + fe = 135 cm (when the final image is at infinity)

L = fo + 4f + ( (feD)/(fe + D) ) = 129.4 cm (when the final image is at near point)

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