Lens Magnification
Image size relative to object size.
Formula
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How it works
Lens magnification tells you how the height of an image compares with the height of the object that produced it. The formula M = -d_i/d_o comes from similar triangles in a thin-lens ray diagram, which link the image and object distances to the size ratio. The minus sign is important because it indicates image orientation: a negative magnification means an inverted image, while a positive value means an upright image.
When to use it
Use this formula when you know the object distance and image distance for a thin lens and want to find how large the image will be compared with the object. It is common in optics problems involving converging or diverging lenses, magnifying glasses, camera lenses, and basic ray-diagram analysis.
Worked example, step by step
A candle is placed 30 cm from a converging lens, and the image forms 45 cm on the other side of the lens. Step 1: Identify the distances: d_o = 30 cm, d_i = 45 cm. Step 2: Substitute into the magnification formula: M = -d_i / d_o. Step 3: Calculate: M = -45 / 30 = -1.5. Step 4: Interpret the result: the image is 1.5 times the object's size and is inverted because the magnification is negative. Final answer: M = -1.5.
Common mistakes to avoid
- Dropping the negative sign and forgetting that it shows image orientation
- Swapping object distance and image distance in the ratio
- Using the formula for image size directly without checking that distances are measured from the lens
Did You Know?
Magnification greater than one enlarges, while a negative value flips the image upside down.
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