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Mirrors and Image Formation — Concave vs Convex

High School⏱ 10 min readOptics

Concave and convex mirrors: how curved mirrors form real and virtual images, the mirror equation 1/f = 1/do + 1/di, and ray diagrams explained.

Quick answer

Curved mirrors shape images with geometry: concave mirrors converge light and can form real or magnified images; convex mirrors diverge light and always give small upright virtual images. The mirror equation 1/f = 1/do + 1/di locates any image.

1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Unit: All distances in the same length unit

Example: Hold a spoon's inner (concave) side close to your face and your reflection is magnified and upright; move it far away and the image flips upside down — the object crossed the focal point.

What you will learn

  • Distinguish concave, convex, and plane mirrors by shape and behavior
  • Use the mirror equation to locate images
  • Draw the three principal rays for curved mirrors
  • Classify images as real/virtual, upright/inverted, magnified/minified
  • Explain everyday uses of each mirror type

Bend the mirror, bend the image

A plane mirror gives an honest, life-size reflection. Bend the mirror and honesty ends — curved mirrors stretch, shrink, flip, and focus light. Yet everything they do follows from the same law of reflection, applied to a curved surface.

  • Concave (caved inward): converges reflected rays, like a satellite dish for light.
  • Convex (bulging outward): diverges reflected rays, spreading the view wide.
  • Plane: the flat special case — virtual, upright, same-size images.

Focal length of a spherical mirror

For spherical mirrors, the focal length is half the radius of curvature:

Sign convention (real-is-positive)

Distances measured in front of the mirror are positive. Concave f > 0, convex f < 0. Positive di → real image in front; negative di → virtual image behind.

The mirror equation

The mirror equation locates every image:

Worked example. A concave mirror has f = 20 cm. An object sits 30 cm in front. Where is the image?

1di=120−130=3−260=160\frac{1}{d_i} = \frac{1}{20} - \frac{1}{30} = \frac{3-2}{60} = \frac{1}{60}

di=60d_i = 60 cm — a real, inverted image 60 cm in front of the mirror. Magnification m=−di/do=−2m = -d_i/d_o = -2: twice as tall and upside down.

Ray diagrams: three rays predict everything

Three rays tell the whole story for any curved mirror:

  1. A ray parallel to the axis reflects through the focal point (concave) or as if from it (convex).
  2. A ray through the focal point reflects parallel to the axis.
  3. A ray hitting the vertex (mirror center) reflects symmetrically, like a plane mirror.

Where any two meet — or appear to meet — sits the image. Sketch these and you can predict every case: magnified shaving-mirror selfies, inverted telescope images, minified security-mirror views.

Why each shape earns its job

Convex mirrors trade size for field of view: the image is always virtual, upright, and smaller — but you see far more of the world. That is why shops, driveways, and car side mirrors use them.

Concave mirrors trade field of view for intensity and magnification: headlight reflectors collimate bulbs into beams, solar furnaces concentrate sunlight to thousands of degrees, and makeup mirrors enlarge your face when you lean inside the focal length.

Variables and units

SymbolNameUnitMeaning
ffFocal lengthm or cmDistance from mirror to focal point
dodoObject distancem or cmDistance from mirror to object
didiImage distancem or cmDistance from mirror to image
mmMagnificationunitlessImage height over object height; negative means inverted

Common mistakes

✗ Concave mirrors always magnify.

Only when the object sits inside the focal length (like a shaving mirror). Farther out, concave mirrors form real, inverted images that can be smaller than the object — that is how reflecting telescopes work.

✗ A virtual image is not really there, so it is useless.

Virtual images are perfectly visible and useful — every plane mirror image is virtual. 'Virtual' only means the rays do not actually converge there; your eye cannot tell the difference.

✗ The focal point is where the image always forms.

The focal point is where parallel incoming rays converge. Images of nearby objects form elsewhere — the mirror equation locates them exactly.

Real-world applications

  • Car headlights: concave reflectors behind the bulb throw parallel beams down the road.

  • Makeup and shaving mirrors: concave mirrors magnify when your face is inside the focal length.

  • Telescopes: large observatories use giant concave mirrors to gather faint starlight.

  • Security mirrors: convex mirrors in shops and driveways give a wide, minified view of a large area.

Frequently asked questions

What is the difference between concave and convex mirrors?

A concave mirror curves inward like a cave and converges light — it can form real, magnified, or virtual images depending on object distance. A convex mirror bulges outward, always diverges light, and always forms small upright virtual images.

What is a real vs virtual image?

A real image forms where reflected rays actually meet — it can be projected on a screen. A virtual image forms where rays only appear to meet behind the mirror — you can see it but never project it.

How do I use the mirror equation?

Use 1/f = 1/do + 1/di with the sign convention: distances in front of the mirror (real side) are positive. For a concave mirror f is positive; for convex, f is negative. A positive di means a real image in front; negative means virtual behind.

Why do car side mirrors say objects are closer than they appear?

Yes — the 'objects in mirror are closer than they appear' warning. Convex mirrors minify, so your brain (expecting normal size) judges the car as farther away than it is.