The object is located at a distance of 50 cm from the thin collecting lens. At what distance from

The object is located at a distance of 50 cm from the thin collecting lens. At what distance from the lens is the image of this object if the dimensions of the image and the object are the same? What is the focal length and power of the lens?

Since, according to the condition of the problem, the dimensions of the object and the image are the same, the focal distance from the lens to the image is equal to the distance from the object to the image:

f = d = 50 cm.

Now you need to use the formula for the focal length of the converging lens and find the focal length:

1 / F = 1 / f + 1 / d → F = 0.25 m = 25 cm.

Let’s substitute in the formula of the optical power of the lens:

D = 1 / F = 1 / 0.25 m = 4 diopters.

Answer: 4 diopters.