How is the magnification of a lens related to the object distance? How is it related to the image distance? What is the significance of the sign of the magnification? What is the significance of its magnitude (size)?

Question: Explain the relationship between magnification, object distance, and image distance, and the significance of the sign and magnitude of the magnification. Answer: The magnification of a lens is given by the equation m = - (v / u), where m is the magnification, v is the image distance, and u is the object distance. An increase in object distance generally leads to a decrease in magnification, while an increase in image distance can either increase or decrease the magnification depending on the sign of the magnification. A positive magnification indicates an upright image, while a negative magnification indicates an inverted image. The magnitude of the magnification informs us whether the image is larger, smaller, or the same size as the object (|m| > 1, |m| < 1, or |m| = 1, respectively).