An astronomical telescope, Fig. 33–36, produces an inverted image. One way to make a telescope that produces an upright image is to insert a third lens between the objective and the eyepiece, Fig. 33–39b. To have the same magnification, the non-inverting telescope will be longer. Suppose lenses of focal length 150 cm, 1.5 cm, and 10 cm are available. Where should these three lenses be placed to make a non-inverting telescope with magnification 100x ?

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1. Identify the role of each lens in the non-inverting telescope setup. The first lens (objective) with the longest focal length (150 cm) is used to gather light and form the initial image. The second lens (erecting lens) with a focal length of 10 cm is used to invert the image back to the upright position. The third lens (eyepiece) with the shortest focal length (1.5 cm) is used to magnify the image formed by the objective lens.
2. Calculate the position of the erecting lens relative to the objective lens. The erecting lens should be placed at a distance equal to the sum of the focal lengths of the objective and the erecting lens from the objective lens. This ensures that the image formed by the objective lens is at the focal point of the erecting lens, allowing the erecting lens to produce an upright image.
3. Determine the position of the eyepiece relative to the erecting lens. The eyepiece should be placed at a distance equal to the sum of the focal lengths of the erecting lens and the eyepiece from the erecting lens. This placement ensures that the upright image formed by the erecting lens is at the focal point of the eyepiece, allowing the eyepiece to magnify the image.
4. Calculate the total length of the telescope. The total length is the sum of the distances from the objective lens to the erecting lens and from the erecting lens to the eyepiece. This gives the overall length of the telescope setup.
5. Verify that the magnification of the telescope is 100x. The magnification is the product of the magnifications provided by the objective and the eyepiece. The magnification provided by the objective lens is the ratio of its focal length to that of the erecting lens, and the magnification provided by the eyepiece is the ratio of the focal length of the erecting lens to that of the eyepiece.