A 4.0 cm tall object is placed 50 cm away from a converging lens of focal length 25 cm. What is the nature and location of the image?
A) The image is real, 2.5 cm tall, 25 cm on the same side as object.
B) The image is real, 4.0 cm tall, 50 cm on the other side of the lens.
C) The image is virtual, 4.0 cm tall, 50 cm on the same side as object.
D) The image is virtual, 2.0 cm tall, 15 cm on the other side of the lens.
E) The image is virtual, 2.5 cm tall, 25 cm on the other side of the lens.

Question

Quizplus · Accepted Answer

Using the lens formula 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance, and the magnification formula m = v/u = h'/h, where h' is the image height and h is the object height, we can find the nature and location of the image. Given f = 25 cm and u = -50 cm (object distance is taken as negative in lens formula), solving for v gives v = 50 cm, indicating the image is formed 50 cm on the other side of the lens. The positive value of v indicates a real image. Using the magnification formula, the image height remains the same (4.0 cm) since the magnification is 1 (v/u = 50/-50 = -1, indicating the image is inverted and the same size as the object). Therefore, the correct answer is that the image is real, 4.0 cm tall, and located 50 cm on the other side of the lens.

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