Free MCAT study note
Concave vs Convex Mirrors: Focal Length Sign, Image Type and Magnification
Check your email
We sent a link to confirm your address. Nothing else is sent until you click it.
Download your free sample: 3-page Amino Acids, Proteins and Enzymes cheat sheet (PDF)
Meanwhile, start with the free notes.
A concave mirror curves inward like a bowl and has a positive focal length. A convex mirror bulges outward and has a negative focal length. The focal length is half the radius of curvature: f = r/2.
The equations
- Mirror equation: 1/f = 1/o + 1/i
- Magnification: m = -i/o = hi/ho
Sign conventions (mirrors)
| Quantity | Positive | Negative |
|---|---|---|
| f, r | Concave (center of curvature in front) | Convex (behind the mirror) |
| o | Object in front (almost always) | Rare |
| i | Real image, in front of the mirror | Virtual image, behind the mirror |
| m | Upright | Inverted |
Real images form where light actually converges, so they can be projected on a screen.
Concave mirror images
| Object position | Image |
|---|---|
| Beyond C (o > 2f) | Real, inverted, smaller |
| At C | Real, inverted, same size |
| Between C and F | Real, inverted, larger |
| At F | No image (rays parallel) |
| Inside F (o < f) | Virtual, upright, larger |
Convex mirror images
Always virtual, upright and smaller, wherever the object sits. That is why they are used for wide-angle views such as car side mirrors.
Worked example
A concave mirror has f = +10 cm and an object at 30 cm. 1/i = 1/10 - 1/30 = 2/30, so i = +15 cm (real). m = -15/30 = -0.5: inverted and half size.
Common traps
- Mixing lens and mirror conventions. For lenses a positive image distance is on the far side; for mirrors a positive image distance is in front.
- Forgetting the minus in m = -i/o.
- Thinking a plane mirror has f = 0. Its focal length is infinite.
One-minute recap
- Concave: f positive. Convex: f negative.
- Positive i means real; negative i means virtual.
- Convex mirrors always give small, upright, virtual images.
Check yourself: 5-question mini-quiz
1. What is the sign of the focal length of a convex mirror?
Negative.
2. What is the relationship between focal length and radius of curvature?
f = r/2.
3. Where must an object be placed for a concave mirror to form a virtual image?
Inside the focal point.
4. What does a negative magnification mean?
The image is inverted.
5. Which mirror type always forms a smaller upright virtual image?
Convex.
Free MCAT sampler
Free sample: a 3-page MCAT cheat sheet (PDF), plus 6 short high-yield lessons by email
Enter your email and download a real page set from a paid pack: the 3-page Amino Acids, Proteins and Enzymes cheat sheet (PDF). Confirm your email and short MCAT lessons follow. Free, no card.
Prefer not to sign up? The sampler is open to everyone: free notes, practice sets and the study schedule generator.
Check your email
We sent a link to confirm your address. Nothing else is sent until you click it.
Download your free sample: 3-page Amino Acids, Proteins and Enzymes cheat sheet (PDF)
Meanwhile, start with the free notes.
Keep studying
- Thin Lens and Mirror Equation: Sign Conventions for the MCAT
- Doppler Effect and Sound Intensity for the MCAT: Formula and Decibels
- Bernoulli's Equation and the Venturi Effect for the MCAT
- Weak Acid and Strong Base Titration Curve: Half-Equivalence Point and Buffer Region
- Types of Radioactive Decay for the MCAT: Alpha, Beta, Gamma, Positron, Electron Capture
- Periodic Table Trends for the MCAT: Radius, Ionization Energy, Electronegativity
- Osmotic Pressure and the van't Hoff Factor: Colligative Properties Calculations
- All free notes