Magnification by Lenses Explained Simply with Easy Examples

Magnification by a lens tells how many times larger or smaller the image appears compared to the object, and whether it is upright. It connects object and image distances to visual effect, which is what we actually see through a magnifier or camera.

A magnifying glass makes small print look bigger, a camera lens makes distant scenes fit on sensor, and a microscope reveals microbes. All are governed by the same magnification relation.

Key Concepts

Linear magnification m: Ratio image height to object height, dimensionless. Positive for erect (in Cartesian sign gives sign accordingly), negative for inverted.

Object distance u, image distance v: Measured from optical centre, metres. Magnification magnitude equals v divided by u magnitude.

Angular magnification: For magnifier, how much bigger angle at eye compared to unaided view, important for instruments.

• m magnitude greater than 1: enlarged
• m magnitude less than 1: diminished
• Concave lens always gives diminished erect virtual image for real object, m between 0 and 1

Formulas

m = height image divided by height object = v divided by u with sign convention. In Cartesian, m = v divided by u. Both v and u in same unit.

Also from lens formula you can find v first, then m. For magnifying glass simple angular magnification approx M = 1 + D divided by f when image at near point D = 25 cm, f in same unit. At infinity, M = D divided by f.

Assumes thin lens and paraxial rays.

Worked Example

Convex lens f = 10 cm forms image 30 cm to right of lens for object left side. Object height 2 cm. Find magnification and image height if object distance is 15 cm left.

1. Cartesian: u = minus 15 cm, v = plus 30 cm (given by lens formula check: 1 divided by 10 = 1 divided by 30 minus 1 divided by minus 15 = 1 divided by 30 plus 1 divided by 15 = 1 divided by 10 correct).
2. m = v divided by u = 30 divided by minus 15 = minus 2.
3. Image height = m times object height = minus 2 times 2 = minus 4 cm. Magnitude 4 cm, inverted, enlarged twice.

This matches projector case: object just outside f gives large real image.

Common Misconceptions

• Magnification always greater than 1 for convex lens: If object beyond 2F, image is diminished between F and 2F. Only inside 2F can be enlarged.
• Negative m means virtual: Sign indicates inverted. Real images from single lens are inverted, virtual magnifier image is erect and positive.
• Power and magnification same: Power is 1 divided by f, magnification depends also on object position, not fixed for a lens.

Real-World Applications

• Magnifying glass uses convex lens with object inside f for erect enlarged virtual image, m positive large
• Camera lens gives diminished inverted real image on small sensor, m magnitude much less than 1
• Microscope combination multiplies objective and eyepiece magnifications for total enlargement
• Projector lens enlarges slide or digital image onto screen, m magnitude many times

Lens magnification m = v divided by u gives size and orientation at a glance. Combine with lens formula to locate image and you fully describe lens behaviour.