Concave vs Convex Mirror: Difference, Uses and Image Formation

Physics · Ray Optics And Optical Instruments · NEET

A concave mirror curves inward and reflects from the inner (caved-in) surface, so it can form both real, inverted images and virtual, erect images depending on where the object is. A convex mirror bulges outward and reflects from the outer surface, so it ALWAYS makes a virtual, erect, diminished image no matter where the object is. Memory hook: "concave = cave you can enter" (light converges, image can be real); "convex = belly pushed out" (light diverges, image always small and virtual).
Concave (converging)Convex (diverging)Frays meet -> real focusFvirtual focus (behind)
Left: a concave mirror bends parallel rays inward so they cross at a real focus F in front of it (converging, f negative). Right: a convex mirror spreads parallel rays apart; they only appear to come from a virtual focus F behind it (diverging, f positive). This is why concave can make real images but convex is always virtual.

Your doubts, answered

Is a concave mirror converging or diverging?

A concave mirror is a CONVERGING mirror. Parallel rays hitting it bounce back and meet at a single point in front of the mirror, called the principal focus F. Because rays actually cross, this focus is real and the focal length is taken as negative in the standard NEET sign convention (f is negative for concave, positive for convex). A convex mirror is the opposite: it is a DIVERGING mirror, the reflected rays spread out and only appear to come from a focus behind the mirror.

Why does a convex mirror always give a virtual image?

In a convex mirror the reflected rays always diverge (spread apart), no matter how close or far the object is. Diverging rays never actually meet in front of the mirror, so no real image can form on a screen. The rays only APPEAR to come from a point behind the mirror, so the eye sees a virtual, erect, and diminished image there. This is why the image in a convex mirror is small and always upright.

Can a concave mirror ever give a virtual image?

Yes. When the object is placed between the pole P and the focus F (that is, closer to the mirror than the focus), a concave mirror gives a VIRTUAL, erect, and magnified image behind the mirror. This is exactly how a shaving mirror or make-up mirror works. But when the object is beyond F, the concave mirror gives a real, inverted image. So concave is the flexible one: it can do both, and NEET loves testing this switch at the focus.

Which mirror is used in a car rear-view mirror and why?

A convex mirror. It always makes a diminished, erect image, so a large area of the road fits into a small mirror, giving the driver a wide field of view behind the vehicle. The trade-off is that objects look smaller and therefore farther away than they really are, which is why side mirrors often carry the warning 'objects in mirror are closer than they appear'. A concave mirror would enlarge and could invert, which is useless for driving.

How do I tell concave from convex mirror by the sign of focal length?

Use the Cartesian sign convention (light travels left to right, distances measured from the pole). For a concave mirror the focus lies in front of the mirror, on the same side as the incoming light, so f is NEGATIVE. For a convex mirror the focus lies behind the mirror, so f is POSITIVE. Quick rule: f negative means concave (converging), f positive means convex (diverging). The radius of curvature R has the same sign, and f = R/2.

Does a concave mirror always magnify?

No. A concave mirror magnifies only for some object positions. Object inside the focus gives an enlarged virtual image; object between F and C (centre of curvature) gives an enlarged real image; object AT C gives a same-size image (m = -1); and object BEYOND C gives a diminished real image. So a concave mirror can shrink, keep, or enlarge the image depending on distance. Only a convex mirror is guaranteed to always diminish.

⚠️ The NEET trap
Assuming a concave mirror always forms a real, inverted image and a convex mirror is 'just the reverse'.
A concave mirror forms a VIRTUAL, erect, magnified image when the object is inside the focus (between P and F). Only when the object is beyond F does it give a real, inverted image. A convex mirror is the only one that is always virtual, erect, and diminished.
🧠 NEET tests the object-inside-focus case on purpose. Remember: concave can be both real and virtual; convex is always virtual. If a question gives m = +2 (magnified and erect), it is a CONCAVE mirror, not convex.

Real NEET questions

2016

Match the entries of Column 1 (m = magnification produced by the mirror) with Column 2. Column 1: (A) m = -2, (B) m = -1/2, (C) m = +2, (D) m = +1/2. Column 2: (a) Convex mirror, (b) Concave mirror, (c) Real image, (d) Virtual image.

A · A -> b,c; B -> b,c; C -> b,d; D -> a,d
B · A -> a,c; B -> a,d; C -> a,b; D -> c,d
C · A -> a,d; B -> b,c; C -> b,d; D -> b,c
D · A -> c,d; B -> b,d; C -> b,c; D -> a,d
Solution: Magnification m = -v/u tells you both nature and mirror. Sign first: m negative means inverted and real image; m positive means erect and virtual image. Then the mirror: a real image can only come from a concave mirror; a diminished erect (positive, |m|<1) image is the signature of a convex mirror. (A) m = -2: negative, so real and inverted, magnified -> concave (b) + real (c). (B) m = -1/2: negative, so real, diminished -> still concave (b) + real (c). (C) m = +2: positive, so virtual, erect, magnified -> concave mirror with object inside focus -> concave (b) + virtual (d). (D) m = +1/2: positive, erect, diminished -> the classic convex mirror case -> convex (a) + virtual (d). Hence A->b,c; B->b,c; C->b,d; D->a,d, which is option A.
2018

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be:

A · 30 cm towards the mirror
B · 36 cm away from the mirror
C · 30 cm away from the mirror
D · 36 cm towards the mirror
Solution: Use the mirror formula 1/v + 1/u = 1/f with the concave-mirror sign convention f = -15 cm. Step 1 (object at 40 cm): u1 = -40 cm. 1/v1 = 1/f - 1/u1 = 1/(-15) - 1/(-40) = -1/15 + 1/40 = (-8 + 3)/120 = -5/120 = -1/24, so v1 = -24 cm. Step 2 (object moved 20 cm towards mirror, now at 20 cm): u2 = -20 cm. 1/v2 = 1/(-15) - 1/(-20) = -1/15 + 1/20 = (-4 + 3)/60 = -1/60, so v2 = -60 cm. Both images are in front of the mirror (v negative = real). Displacement of image = |v2| - |v1| = 60 - 24 = 36 cm, and since the image moved farther from the mirror, it shifts 36 cm AWAY from the mirror. Answer: option B.

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Frequently asked

What is the main difference between a concave and a convex mirror?

A concave mirror reflects from its inner curved (caved-in) surface and converges light, so it can form real or virtual images. A convex mirror reflects from its outer bulging surface and diverges light, so it only ever forms a virtual, erect, diminished image.

Which mirror can form a real image?

Only a concave mirror can form a real image (one that can be caught on a screen), and only when the object is placed at or beyond the focus F. A convex mirror can never form a real image because its reflected rays always diverge.

Is the focal length of a convex mirror positive or negative?

Positive. In the Cartesian sign convention the focus of a convex mirror lies behind the mirror, so f is positive. A concave mirror has its focus in front, so f is negative. In both cases f = R/2.

Why do convex mirrors give a wider view?

Because a convex mirror always shrinks the image, a large scene fits into a small mirror. This wide field of view is why convex mirrors are used as vehicle rear-view mirrors, at road bends, and in shop security mirrors.

Where should an object be placed in a concave mirror to get a magnified erect image?

Place the object between the pole and the focus (inside F). Then the concave mirror gives a virtual, erect, and magnified image, which is how a shaving or make-up mirror works.