At what distance from a lens with an optical power of 2 diopters should the screen be placed in order to get

At what distance from a lens with an optical power of 2 diopters should the screen be placed in order to get a sharp image of an object located in front of the lens at a distance of 2 m?

Replace in the thin lens formula: 1 / F = 1 / d + 1 / f, where F is the focal length of the lens, d is the distance from the object to the lens, f is the distance from the image to the lens obtained with this lens, 1 / F on D, since 1 / F = D, D is the optical power of the lens. We get 1 / d + 1 / f = D; f = d / (D ∙ d – 1). From the condition of the problem it is known that the object is located in front of the lens with an optical power D = 2 diopters at a distance d = 2 m.We substitute the values ​​of physical quantities in the formula to determine at what distance from the lens f the screen must be placed in order to obtain a sharp image on it, and make calculations: f = 2 / (2 ∙ 2 – 1); f = 2/3 (m).
Answer: at a distance of 2/3 meters from the lens, you need to place a screen in order to get a sharp image on it.