In a thin lens with object distance do and image distance di, the thin-lens equation and the transverse magnification are respectively given by which expressions?

In a thin lens with object distance do and image distance di, the thin-lens equation and the transverse magnification are respectively given by which expressions?

• A. 1/f = 1/do + 1/di; m = do/di
• B. 1/f = 1/do + 1/di; m = - di/do
• C. f = do + di; m = di/do
• D. 1/f = 1/di - 1/do; m = - do/di

Answer: (B)

The main concept here is how a thin lens relates distances and how the image size compares to the object size. With the standard sign convention, the thin-lens equation is 1/f = 1/do + 1/di, where do is the object distance, di is the image distance, and f is the focal length (positive for a converging lens, with real images having positive di). The transverse magnification m, defined as the ratio of image height to object height, is m = hi/ho = - di/do. The negative sign shows that a real image is inverted relative to the object when a real image forms. Therefore, the expression with 1/f = 1/do + 1/di and m = - di/do matches the standard relations. The other forms either mix up signs, omit the negative for inversion, or state a nonsensical or incorrect relation like f = do + di, which isn’t dimensionally or conceptually correct in this context.

The main concept here is how a thin lens relates distances and how the image size compares to the object size. With the standard sign convention, the thin-lens equation is 1/f = 1/do + 1/di, where do is the object distance, di is the image distance, and f is the focal length (positive for a converging lens, with real images having positive di). The transverse magnification m, defined as the ratio of image height to object height, is m = hi/ho = - di/do. The negative sign shows that a real image is inverted relative to the object when a real image forms. Therefore, the expression with 1/f = 1/do + 1/di and m = - di/do matches the standard relations. The other forms either mix up signs, omit the negative for inversion, or state a nonsensical or incorrect relation like f = do + di, which isn’t dimensionally or conceptually correct in this context.