JAMB Physics 2019 Paper

Concept:For a convex lens forming a real image, the lens formula and magnification relate object distance $u$, image distance $v$, and focal length $f$.Explanation:Let the object distance be $u$ and the image distance be $v$.The distance between object and real image is given as:$$u + v = 40$$Magnification is $3$, so for a real image:$$\frac{v}{u} = 3$$$$v = 3u$$Substitute into the distance equation:$$u + 3u = 40$$$$4u = 40$$$$u = 10 \text{ cm}$$Then:$$v = 3u = 30 \text{ cm}$$Using the lens formula:$$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$$$$\frac{1}{f} = \frac{1}{10} + \frac{1}{30} = \frac{3 + 1}{30} = \frac{4}{30}$$$$f = \frac{30}{4} = 7.5 \text{ cm}$$Answer:The focal length of the lens is $7.5 \text{ cm}$, so the correct option is B.