Linear magnification calculator

Linear magnification says how many times larger or smaller the image is than the object, measured along the optical axis. The formula is a ratio of distances: p = y/x. Field y is the image distance (numerator), field x is the object distance (denominator). A school magnifier uses a different rule, M = 25 cm/f + 1, and that one takes focal length, not a y and x pair.

Put a projector on the bench. Image 60 cm behind the lens, object 30 cm in front. y = 0.6 m, x = 0.3 m, p = 2. The image is twice as far and twice as large in this model. Flip the numbers: y = 0.1 m and x = 0.2 m give p = 0.5, image closer to the glass and smaller than the object. When y = x, for example both 0.4 m, p = 1 and the scale is one to one.

Both distances have to be positive and in the same unit. p is a pure number, so the meter/foot switch only changes the labels, not the result. The pair 2 m and 0.1 m gives p = 20, like a large screen. The pair 52 mm and 2 m gives p = 0.026, like a frame on a sensor. Beside p sits |p|; here they match, because p > 0.

On the form, y comes first because that is how the formula is written. Type the image, then the object, then Calculate. The calculator example 0.6 and 0.3 gives 2. A comma and a period both parse. The chart of p versus y at fixed x is a straight line: double y, double p.

Feed the same x and y into the lens page. At 0.6 m and 0.3 m you get f = 0.2 m there, because 1/0.3 + 1/0.6 = 5. Here you stay with the ratio. A minus sign for an inverted image appears in p in another convention. Here both distances are positive, so p is positive; you describe inversion in words.

A microscope multiplies objective and eyepiece magnifications. Here one y/x pair, one lens. p is not brightness: a twice-larger image is not twice the lumens.