{"id":460,"date":"2026-07-12T01:31:12","date_gmt":"2026-07-12T01:31:12","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=460"},"modified":"2026-07-12T01:31:13","modified_gmt":"2026-07-12T01:31:13","slug":"concave-convex-mirror","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/waves\/concave-convex-mirror\/","title":{"rendered":"Concave vs Convex Mirror"},"content":{"rendered":"\n
Definition<\/div>

\n\nConcave and convex mirror surfaces curve in opposite directions: a concave mirror curves inward and converges reflected light to a real focus, while a convex mirror bulges outward and makes light diverge from a virtual focus behind it. Both obey the mirror equation: one over f equals one over v plus one over u. Convex images are always virtual.\n\n<\/p><\/div>\n\n

Pick up a metal spoon and look at your face in the hollow side. You are upside down. Turn the spoon over, look at the back, and there you are again \u2014 the right way up, small, and slightly squashed. Same spoon. Same light. Same eyes.<\/p>\n\n

Nothing about you changed. What changed was which way the reflecting surface curved \u2014 and that single geometric fact decides whether light comes together or spreads apart. It is the whole of this article in one piece of cutlery.<\/p>\n\n

What Is a Concave and Convex Mirror?<\/h2>\n\n

Start with the shape, because everything else follows from it. Both mirrors are cut from the surface of an imaginary sphere; the only question is which side of that sphere is silvered.<\/p>\n\n

A concave mirror<\/strong> is silvered on the outside of the sphere, so the reflecting surface caves inward, away from you. Rays arriving parallel to the axis are folded toward one another and cross at a genuine point in space.<\/p>\n\n

A convex mirror<\/strong> is silvered on the inside, so the reflecting surface bulges outward, toward you. Parallel rays are thrown apart. Trace them backwards and they seem to stream out of a point behind the glass \u2014 a point no light ever actually reaches.<\/p>\n\n

That is the entire distinction. A concave mirror is a converging<\/em> mirror; a convex mirror is a diverging<\/em> mirror.<\/p>\n\n\n <\/rect>\n\n CONCAVE \u2014 converging<\/text>\n CONVEX \u2014 diverging<\/text>\n\n <\/line>\n <\/path>\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n\n <\/circle>\n F<\/text>\n Real focus, f > 0<\/text>\n Light really passes through F<\/text>\n\n <\/line>\n <\/path>\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/line>\n\n <\/circle>\n F<\/text>\n Virtual focus, f < 0<\/text>\n No light reaches F<\/text>\n<\/svg>\n\n

Parallel light on a concave and convex mirror. Solid gold lines are real rays; dashed lines are backward extensions that never carry energy.<\/p>\n\n

A mnemonic that actually survives the exam<\/h3>\n\n

Concave caves in<\/em>. Stand a torch in front of one and the beam is pulled together; stand in front of a convex one and the beam is pushed away.<\/p>\n\n

If you would rather anchor it to something you own: the inside bowl of a spoon is concave, the polished back is convex. Everything below is that spoon, done with algebra.<\/p>\n\n

Concave and Convex Mirror: 6 Key Differences at a Glance<\/h2>\n\n

Six properties separate the two mirrors, and the first one drives all the others.<\/p>\n\n

\n\n\n\n\n\n\n\n\n\n\n\n
Property<\/th>\nConcave mirror<\/th>\nConvex mirror<\/th>\n<\/tr>\n<\/thead>\n
1. Surface shape<\/strong><\/td>\nCurves inward (caves away from the object)<\/td>\nBulges outward (toward the object)<\/td>\n<\/tr>\n
2. Effect on parallel rays<\/strong><\/td>\nConverges them<\/td>\nDiverges them<\/td>\n<\/tr>\n
3. Focus and sign of f<\/strong><\/td>\nReal focus in front; f is positive<\/strong><\/td>\nVirtual focus behind; f is negative<\/strong><\/td>\n<\/tr>\n
4. Image type possible<\/strong><\/td>\nReal or<\/em> virtual, depending on where the object sits<\/td>\nVirtual only \u2014 always, with no exception<\/td>\n<\/tr>\n
5. Orientation and size<\/strong><\/td>\nInverted and diminished, same-size, or magnified \u2014 six distinct cases<\/td>\nUpright and diminished, every single time<\/td>\n<\/tr>\n
6. Field of view<\/strong><\/td>\nNarrow<\/td>\nWide \u2014 the reason it is a safety mirror<\/td>\n<\/tr>\n
Best uses<\/strong><\/td>\nShaving mirrors, dentist’s mirrors, headlamp reflectors, solar cookers, telescope primaries<\/td>\nPassenger-side wing mirrors, shop security mirrors, blind-corner road mirrors, ATM mirrors<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

Row 4 is the one worth memorising. A convex mirror producing a real image is not a hard problem \u2014 it is an impossible one, and later on we will prove it in three lines of algebra.<\/p>\n\n

The Mirror Formula: 1\/f = 1\/v + 1\/u<\/h2>\n\n

One equation covers both mirrors. Nothing switches; only the sign of f<\/em> changes.<\/p>\n\n

1\/f = 1\/v + 1\/u<\/div>\n\n

The focal length is fixed by the sphere the mirror was cut from:<\/p>\n\n

f = R\/2<\/div>\n\n

And the magnification links the two heights to the two distances:<\/p>\n\n

m = h_i \/ h_o = \u2212v \/ u<\/div>\n\n

Every symbol, with its unit<\/h3>\n\n
\n\n\n\n\n\n\n\n\n\n\n\n
Symbol<\/th>\nQuantity<\/th>\nSI unit<\/th>\nSign rule<\/th>\n<\/tr>\n<\/thead>\n
u<\/strong><\/td>\nObject distance from the pole<\/td>\nmetre (m)<\/td>\nAlways positive for a real object<\/td>\n<\/tr>\n
v<\/strong><\/td>\nImage distance from the pole<\/td>\nmetre (m)<\/td>\nPositive if in front (real); negative if behind (virtual)<\/td>\n<\/tr>\n
f<\/strong><\/td>\nFocal length<\/td>\nmetre (m)<\/td>\nPositive for concave; negative for convex<\/td>\n<\/tr>\n
R<\/strong><\/td>\nRadius of curvature<\/td>\nmetre (m)<\/td>\nSame sign as f, since R = 2f<\/td>\n<\/tr>\n
ho<\/sub><\/strong><\/td>\nObject height<\/td>\nmetre (m)<\/td>\nTaken as positive (upright object)<\/td>\n<\/tr>\n
hi<\/sub><\/strong><\/td>\nImage height<\/td>\nmetre (m)<\/td>\nPositive if upright; negative if inverted<\/td>\n<\/tr>\n
m<\/strong><\/td>\nLinear magnification<\/td>\ndimensionless<\/td>\nm > 0 upright; m < 0 inverted; |m| > 1 magnified<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

Any consistent unit works \u2014 centimetres throughout, or metres throughout. Mixing them is the single most common arithmetic disaster in this topic.<\/p>\n\n

Pin the sign convention down before you substitute<\/h3>\n\n

Different textbooks measure distances from different origins, and both give correct answers if you never mix them<\/em>. This article uses the real-is-positive convention above, which is also what our calculator uses.<\/p>\n\n

In practice, the slip that costs marks is subtle. A student half-remembers a Cartesian convention where u<\/em> is negative, writes u<\/em> = \u221230 cm, but then also writes f<\/em> = +10 cm for a concave mirror out of habit. Two conventions in one equation, and the two errors do not cancel.<\/p>\n\n

Choose one convention. Write the signs down before you touch the algebra. You can also check any answer instantly with our Lens & Mirror Calculator<\/a>, which solves the mirror equation for focal length, either distance or the magnification and shows every step of the working.<\/p>\n\n

Why is the focal length exactly half the radius?<\/h3>\n\n

Take a ray parallel to the axis, striking the mirror at a height h<\/em> above it. The normal at that point runs along the radius, straight back to the centre of curvature C.<\/p>\n\n

The law of reflection makes the reflected ray leave at the same angle to that normal. Simple geometry then puts the crossing point on the axis at exactly half of R \u2014 but only when h<\/em> is small compared with R, so that the angles stay small.<\/p>\n\n

This is the paraxial approximation<\/strong>, and f = R\/2 lives or dies by it. Rays that strike far from the axis cross the axis a little closer to the mirror, smearing the focus. Opticians call that spherical aberration<\/em>, and it is precisely why serious telescope mirrors are ground into paraboloids rather than spheres.<\/p>\n\n

How Concave and Convex Mirrors Form Images<\/h2>\n\n

You do not need a protractor. Three standard rays are enough, and any two of them fix the image.<\/p>\n\n

    \n
  • Ray 1 \u2014 parallel in, through F out.<\/strong> A ray arriving parallel to the axis reflects through the focus (concave) or appears to come from the focus (convex).<\/li>\n
  • Ray 2 \u2014 through F in, parallel out.<\/strong> The reverse of ray 1, because light paths are reversible.<\/li>\n
  • Ray 3 \u2014 strike the pole.<\/strong> At the pole the mirror is locally flat and the axis is the normal, so the ray reflects at an equal angle on the other side of the axis.<\/li>\n<\/ul>\n\n

    Where the reflected rays actually meet, you get a real image<\/strong> \u2014 catchable on a screen. Where only their backward extensions meet, you get a virtual image<\/strong> \u2014 visible to the eye, but with no light at that location.<\/p>\n\n\n <\/rect>\n\n CONCAVE \u2014 object beyond C<\/text>\n\n <\/line>\n principal axis<\/text>\n\n <\/path>\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/polygon>\n Object<\/text>\n\n <\/line>\n <\/polygon>\n Image<\/text>\n real \u00b7 inverted \u00b7 diminished<\/text>\n\n <\/circle>\n C<\/text>\n <\/circle>\n F<\/text>\n <\/circle>\n P<\/text>\n\n <\/line>\n\n CONVEX \u2014 any object position<\/text>\n\n <\/rect>\n behind the mirror<\/text>\n\n <\/line>\n\n <\/path>\n <\/line>\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/line>\n <\/line>\n\n <\/line>\n <\/polygon>\n Object<\/text>\n\n <\/line>\n <\/polygon>\n Image<\/text>\n virtual \u00b7 upright \u00b7 diminished<\/text>\n\n <\/circle>\n P<\/text>\n <\/circle>\n F<\/text>\n <\/circle>\n C<\/text>\n<\/svg>\n\n

    Ray diagrams for a concave and convex mirror. Solid rays carry light; dashed lines are extensions behind the convex mirror, where the virtual image sits.<\/p>\n\n

    The six cases of a concave mirror<\/h3>\n\n

    Slide the object along the axis and the image changes character six times. This table is worth knowing cold.<\/p>\n\n

    \n\n\n\n\n\n\n\n\n\n\n
    Object position<\/th>\nImage position<\/th>\nNature<\/th>\nOrientation<\/th>\nSize<\/th>\n<\/tr>\n<\/thead>\n
    At infinity<\/td>\nAt F<\/td>\nReal<\/td>\nInverted<\/td>\nA point<\/td>\n<\/tr>\n
    Beyond C (u > 2f)<\/td>\nBetween F and C<\/td>\nReal<\/td>\nInverted<\/td>\nDiminished<\/td>\n<\/tr>\n
    At C (u = 2f)<\/td>\nAt C<\/td>\nReal<\/td>\nInverted<\/td>\nSame size<\/td>\n<\/tr>\n
    Between C and F<\/td>\nBeyond C<\/td>\nReal<\/td>\nInverted<\/td>\nMagnified<\/td>\n<\/tr>\n
    At F (u = f)<\/td>\nAt infinity<\/td>\nNo image forms<\/td>\n\u2014<\/td>\n\u2014<\/td>\n<\/tr>\n
    Between F and P (u < f)<\/td>\nBehind the mirror<\/td>\nVirtual<\/td>\nUpright<\/td>\nMagnified<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

    A convex mirror needs no such table. Its image is always virtual, always upright, always smaller, and always squeezed into the gap between the pole and the focus.<\/p>\n\n

    <\/span>Concave and Convex Mirror Lab<\/span><\/div>