A convex lens forms a real image when the object is placed at do = 2f. Where is the image, and what are its orientation and size?

• A. di = f; image virtual, upright, smaller
• B. di = 2f; real, inverted, same size
• C. di = 4f; upright
• D. No image formed

Answer: (D)

When a convex lens forms an image, the position of the image is found from the lens equation 1/f = 1/do + 1/di, and the enlargement or reduction from the magnification m = -di/do (the negative sign tells us about orientation). Here the object distance is do = 2f. Plugging in: 1/f = 1/(2f) + 1/di, which gives 1 = 1/2 + f/di, so di = 2f.

This means the image sits on the opposite side of the lens at a distance of 2f, so it is a real image. The magnification is m = -di/do = -2f/2f = -1, which means the image is inverted and has the same size as the object. So the correct description is a real, inverted image located 2f from the lens, with the same height as the object. The other descriptions don’t satisfy the lens equation for do = 2f.