The focal length of the collecting lens is 20 cm, the distance from the object

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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