A student places a candle at a distance greater than twice the focal length from a convex lens. She observes the image formed on a screen. Which of the following best describes the image's nature, position, and size?
The image is real, inverted, formed between the focal point and twice the focal length, and smaller than the object.
For a thin convex lens, the nature, size and position of the image depend on where the object is placed relative to the focal point F and the centre of curvature (at distance 2F). The image forming on a screen is the key clue: only a real image can actually be caught on a screen, so the answer must be a real image.
When the object is placed beyond 2F, the ray diagram (or the lens formula \(\dfrac{1}{v} - \dfrac{1}{u} = \dfrac{1}{f}\)) shows the image forming on the far side of the lens, between F and 2F. The image is real, inverted, and diminished (smaller than the object).
Hence, the image is real, inverted, formed between the focal point and twice the focal length, and smaller than the object.
A virtual image at the focal point of the same size is not a standard convex-lens case and cannot be caught on a screen. An erect, same-size real image beyond 2F is impossible because a convex lens always inverts a real image. A virtual, erect, magnified image on the object's side is what forms only when the object is placed inside the focal length (as in a magnifying glass), not beyond 2F.
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