Determine the focal length of the diffusing lens if the object is at a distance

Determine the focal length of the diffusing lens if the object is at a distance of 30 cm from the lens, and its image is at a distance of 15 cm from the lens.

For a thin lens, the formula 1 / F = 1 / d + 1 / f is valid, 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, then F = ( d + f) / (d ∙ f). For a diffusing lens, F <0, since such a lens always produces a virtual image, then f <0. From the condition of the problem it is known that the object is at a distance of d = 30 cm = 0.3 m from the lens, and its image is at a distance f = – 15 cm = – 0.15 m from the lens. Substitute the values ​​of physical quantities in the formula and make calculations: F = (0.3 – 0.15) / (0.3 ∙ (- 0.15)); F = – 10/3 ≈ – 3.3 (m).
Answer: The focal length of the diffusing lens is ≈ – 3.3 meters.