Magnification for a lens is defined as m = v ⁄ u, the ratio of image distance to object distance (in the Cartesian sign convention), and it also equals the ratio of image height to object height. A positive m indicates an erect image, and |m| > 1 indicates the image is magnified.

Apply the sign convention (distances measured from the lens, real-object side taken as negative):

• Object distance: u = −10 cm
• Image on the same side as the object (a virtual image): v = −30 cm

So m = v ⁄ u = (−30) ⁄ (−10) = +3.

The image is therefore virtual, erect and three times magnified. We can also confirm the lens type using 1 ⁄ f = 1 ⁄ v − 1 ⁄ u = 1 ⁄ (−30) − 1 ⁄ (−10) = −1 ⁄ 30 + 1 ⁄ 10 = 2 ⁄ 30 = 1 ⁄ 15, giving f = +15 cm. A positive focal length means this is a converging (convex) lens with the object placed within its focal length — exactly how a magnifying glass produces an enlarged upright image.

The negative choices (−3, −0.3) would imply an inverted image, and 0.3 would imply a diminished image; neither matches a virtual, magnified image. The correct answer is 3.