Magnification tells you how many times bigger (or smaller) the image is than the object:m = image height / object height = v / u where v is the image distance and u is the object distance from the lens. Magnification is a ratio of two lengths, so it has no units.If m is greater than 1, the image is larger than the object (magnified). If m is less than 1, the image is smaller (diminished). If m = 1, the image is the same size. When using v/u, use the sizes of the distances; the sign of v tells you whether the image is real or virtual, not how big it is.Worked example 1: an object 4.0 cm tall is 30 cm from a convex lens, and the image forms at v = 15 cm.
m = 15 / 30 = 0.50, so the image height is 0.50 × 4.0 = 2.0 cm. The image is diminished.Worked example 2: a magnifying glass (f = 10 cm) is held 5.0 cm from a stamp. From the lens equation the image is virtual at 10 cm. m = 10 / 5.0 = 2.0, so the stamp looks twice as big.Worked example 3: a projector makes a 1.2 m tall image of a 24 mm tall slide. m = 1.2 / 0.024 = 50.Using the two forms together is powerful: if you know u, v and the object height, you can find the image height, or you can find v from the two heights and u.
m = 15 / 30 = 0.50, so the image height is 0.50 × 4.0 = 2.0 cm. The image is diminished.Worked example 2: a magnifying glass (f = 10 cm) is held 5.0 cm from a stamp. From the lens equation the image is virtual at 10 cm. m = 10 / 5.0 = 2.0, so the stamp looks twice as big.Worked example 3: a projector makes a 1.2 m tall image of a 24 mm tall slide. m = 1.2 / 0.024 = 50.Using the two forms together is powerful: if you know u, v and the object height, you can find the image height, or you can find v from the two heights and u.