# 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. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.