Magnification by Mirrors Explained Simply with Easy Examples

Magnification tells us how much bigger or smaller an image is compared to the object. For mirrors, it also tells us whether the image is upright or inverted. Knowing magnification helps us design mirrors for shaving, telescopes and vehicle safety.

When you look into a concave mirror close up, your face looks larger. When you look into a convex mirror in a car, the view is wider but objects look smaller. Both effects are described by one simple ratio.

Key Concepts

Linear magnification m: Ratio of image height to object height. It has no unit. Positive m means erect image, negative m means inverted image.

Object distance u and image distance v: Measured from the pole of the mirror in metres or centimetres. In the common school sign convention, distances in front of the mirror are negative.

Focal length f: Distance from pole to focus. For concave mirror f is negative, for convex f is positive in this convention.

• m greater than 1: image enlarged
• m less than 1: image diminished
• m equal to 1: same size, as in plane mirror

Formulas

m = height of image divided by height of object = h prime divided by h. Heights are in same unit, so m is dimensionless.

m = minus v divided by u. Here v is image distance, u is object distance, both with sign. This relation comes from similar triangles in the ray diagram. It holds for concave and convex mirrors.

Mirror formula: 1 divided by f = 1 divided by v plus 1 divided by u. Use this first to find v, then find m. All distances must use the same sign convention.

Worked Example

An object 4 cm tall is placed 20 cm in front of a concave mirror of focal length 15 cm. Find image position, size and nature. Use sign convention where in front is negative, so u = minus 20 cm, f = minus 15 cm.

1. Use mirror formula: 1 divided by v = 1 divided by f minus 1 divided by u = 1 divided by minus 15 minus 1 divided by minus 20 = minus 1 divided by 15 plus 1 divided by 20 = minus 1 divided by 60.
2. So v = minus 60 cm. Negative means 60 cm in front of mirror, real image.
3. m = minus v divided by u = minus (minus 60) divided by minus 20 = minus 3.
4. Image height = m times object height = minus 3 times 4 = minus 12 cm. Magnitude 12 cm, sign shows inverted, enlarged 3 times.

The image is real, inverted and 12 cm tall, formed 60 cm in front of the mirror.

Common Misconceptions

• Negative magnification means smaller: Sign only shows orientation. Size is given by absolute value. m = minus 0.5 means inverted and half size.
• Plane mirror can magnify: Plane mirror always gives m = +1. It never enlarges or reduces.
• m = v divided by u without minus: The minus sign is essential. Forgetting it flips erect and inverted predictions.

Real-World Applications

• Concave shaving and makeup mirrors use m greater than 1 for a larger face view
• Convex security mirrors in shops use m less than 1 to cover a wide area
• Car side mirrors are convex, diminished images give wider field despite smaller size
• Reflecting telescopes use large concave mirrors with controlled magnification

Magnification m = h prime divided by h = minus v divided by u captures size and orientation in one number. Learn its sign and magnitude and mirror problems become straightforward.