The focal length of the lens is 0.1 m if the image given by the lens is inverted

The focal length of the lens is 0.1 m if the image given by the lens is inverted and real and reduced by 3 times, then the distance from the object to the image is equal to …

Decision.
Let us replace in the formula of a thin lens: 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, f is G ∙ d, since the magnification of the lens is G = f / d. We get 1 / F = 1 / d + 1 / (G ∙ d), we express d = F ∙ (G + 1) / G, then the distance from the object to the image will be:
d + f = d + G ∙ d;
d + f = (G + 1) ∙ d;
d + f = (G + 1) ∙ F ∙ (G + 1) / G;
d + f = F ∙ (G + 1) ² / G.
From the condition of the problem it is known that the focal length of the lens is F = 0.1 m, the image given by the lens is inverted and real and reduced by 3 times, that is, G = 1/3. Substitute the values ​​of physical quantities in the formula and make calculations to find the distance from the object to the image:
d + f = 0.1 ∙ (1/3 + 1) ² / (1/3);
d + f = 8/15 m.
Answer: The distance from the subject to the image is 8/15 meters.