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The distance between the two lenses in an astronomical telescope is 157 cm. It has a magnification of -44.0 .(a) Determine the focal length of the eyepiece. (b) Determine the focal length of the objective.

Question

The distance between the two lenses in an astronomical telescope is 157 cm. It has a magnification of -44.0 .(a) Determine the focal length of the eyepiece. (b) Determine the focal length of the objective.

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Solution

To solve this problem, we need to use the formula for magnification in a telescope, which is -f_o/f_e, where f_o is the focal length of the objective lens and f_e is the focal length of the eyepiece lens. The negative sign indicates that the image is inverted.

(a) To find the focal length of the eyepiece, we rearrange the formula to solve for f_e: f_e = -f_o/magnification. We don't know f_o yet, but we know that the distance between the two lenses is equal to the sum of their focal lengths (f_o + f_e = 157 cm). We can substitute this into our equation to get f_e = -(157 - f_e)/44. Solving this equation for f_e gives us f_e = 157/(44+1) = 3.5 cm.

(b) Now that we know f_e, we can find f_o by subtracting f_e from the total distance between the lenses: f_o = 157 - 3.5 = 153.5 cm.

This problem has been solved

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To determine the calculated image distance, we used the formula 𝑑𝑖=𝑑𝑜⋅𝑓1𝑑𝑜−𝑓1d i​ = d o​ −f 1​ d o​ ⋅f 1​ ​ . For the image distance after the second lens, a similar formula was applied, but instead of using the object distance directly, we used the difference between the distance from the first lens and the location of the image formed by the first lens as the effective object distance. This was expressed as 𝑑𝑜′=𝑑𝑙𝑒𝑛𝑠−𝑑𝑖d o′​ =d lens​ −d i​ . We also computed the magnification for each lens using both theoretical predictions and experimental data. The theoretical magnification was calculated by dividing the image distance by the object distance. This process was applied to both lenses, with the image formed by the first lens serving as the object for the second lens in our calculations.

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