The focal length of the collecting lens is 20 cm, the distance from the object to the front focus is 5 cm Find the height of the object if the height of the actual object is 10 cm.
Initial data: F (focal length) = 20 cm; x (distance between the front focus and the mounted object) = 5 cm; H (height of actual image) = 10 cm.
1) Calculate the distance from a given lens to the image: 1 / F = 1 / d + 1 / f, whence 1 / f = (d – F) / (d * F) = (F + x – F) / ((F + x) * F) = x / ((F + x) * F) and f = (F + x) * F / x = (20 + 5) * 20/5 = 100 cm.
2) Find the height of the installed object: H / h = f / d, whence h = H * d / f = 10 * (20 + 5) / 100 = 2.5 cm.
Answer: The height of the installed item is 2.5 cm.
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