Ever wondered why a shaving mirror makes your face look bigger, while a camera lens can zoom in on a distant bird?
In simple words, mirrors and lenses bend light rays so that they form images. Depending on the shape, the image can be real (you could catch it on a screen) or virtual (you only see it by looking through the glass).
Concave Mirrors – How They Work
A concave mirror is a curved piece of glass that bulges inward, like the inside of a spoon. When parallel rays hit it, they converge (come together) at a point called the focus. The focus is the spot where the light would meet if you extended the reflected rays backwards.
Mirror formula links object distance (u), image distance (v) and focal length (f):
1/f = 1/v + 1/u
All distances are measured from the mirror’s pole (the centre of the surface). Remember the sign convention – distances measured against the direction of incoming light are negative. So for a real object placed in front of a concave mirror, u is negative.
Worked Example
Object height = 2 cm, object distance u = -30 cm, focal length f = -15 cm (negative because the focus lies in front of the mirror). Plug into the mirror formula:
1/(-15) = 1/v + 1/(-30) → -0.0667 = 1/v - 0.0333 → 1/v = -0.0334 → v ≈ -30 cm.
Image distance is -30 cm, meaning the image forms at the same distance in front of the mirror. Magnification m = v/u = (-30)/(-30) = 1, so the image is same size as the object and upright (virtual because m is positive).
Convex Mirrors – Quick Overview
Convex mirrors bulge outward, like the back of a spoon. They always produce virtual, upright, and reduced images because the reflected rays diverge (spread apart). The focus is behind the mirror, so the focal length is taken as positive.
Mirror formula stays the same, but f > 0 and v is always positive (virtual image behind the mirror).
Example
u = -20 cm, f = +10 cm.
1/10 = 1/v + 1/(-20) → 0.1 = 1/v - 0.05 → 1/v = 0.15 → v ≈ +6.67 cm. Image is 6.67 cm behind the mirror, upright and smaller.
Lenses – Concave (Diverging) and Convex (Converging)
Lenses are transparent pieces of glass that bend light by refraction (change of direction when light passes from one medium to another). A convex lens is thicker in the middle, like a magnifying glass; it brings parallel rays to a real focus on the other side. A concave lens is thinner in the middle; it spreads rays apart, creating a virtual focus on the same side as the object.
Lens formula mirrors the mirror formula:
1/f = 1/v - 1/u
Note the minus sign before 1/u – it comes from the way we define object distance for lenses. Sign convention: object distance u is always negative (object is on the incoming side), focal length f is positive for convex (converging) lenses and negative for concave (diverging) lenses.
Worked Example – Convex Lens
u = -25 cm, f = +12.5 cm.
1/12.5 = 1/v - 1/(-25) → 0.08 = 1/v + 0.04 → 1/v = 0.04 → v = +25 cm. Image forms 25 cm on the other side, real, inverted, and same size as the object.
Worked Example – Concave Lens
u = -30 cm, f = -15 cm.
1/(-15) = 1/v - 1/(-30) → -0.0667 = 1/v + 0.0333 → 1/v = -0.1 → v = -10 cm. Image is virtual, upright, and reduced, located 10 cm in front of the lens.
Comparison Table – Mirrors vs Lenses
| Feature | Concave Mirror | Convex Mirror | Convex Lens | Concave Lens |
|---|---|---|---|---|
| Shape | Inward curve | Outward curve | Thicker centre | Thinner centre |
| Image type | Real or virtual | Always virtual | Real or virtual | Always virtual |
| Focal length sign | - (focus in front) | + (focus behind) | + (converging) | - (diverging) |
| Common use | Telescopes, headlights | Vehicle side‑mirrors | Eyeglasses, cameras | Minus‑power glasses |
Common Mistakes & Quick Tips
- Never forget the sign convention – a wrong sign flips the whole answer.
- For mirrors, the object distance is always taken negative; for lenses it’s the same.
- Remember that virtual images cannot be projected on a screen.
- When the object is at the centre of curvature (distance = 2f), the image coincides with the object.
- Use the magnification formula m = v/u to check if the image should be upright (positive m) or inverted (negative m).
📝 Likely Exam Questions
- Question: An object 3 cm tall is placed 12 cm in front of a concave mirror of focal length 6 cm. Find the image distance, height and nature.
Answer: Using 1/f = 1/v + 1/u → 1/(-6) = 1/v + 1/(-12) → v = -12 cm. Magnification m = v/u = (-12)/(-12)=1, so image height = 3 cm, upright and virtual. - Question: A convex lens of focal length +10 cm forms a real image on a screen 30 cm away. Where is the object?
Answer: Using 1/f = 1/v - 1/u → 0.1 = 1/30 - 1/u → 1/u = 1/30 - 0.1 = -0.0667 → u = -15 cm (object 15 cm in front of lens). - Question: State two differences between images formed by a concave mirror and a convex lens when the object is placed beyond the focal length.
Answer: Both produce real, inverted images, but the concave mirror’s image appears on the same side as the object, whereas the convex lens’s image appears on the opposite side. - Question: A vehicle side‑mirror (convex) has a focal length of +20 cm. An object 2 m away appears at what distance behind the mirror?
Answer: 1/f = 1/v + 1/u → 1/20 = 1/v + 1/(-2000) → 0.05 = 1/v - 0.0005 → 1/v = 0.0505 → v ≈ +19.8 cm (virtual image behind mirror). - Question: Explain why a diverging lens always produces a virtual image regardless of object position.
Answer: A diverging lens spreads incident rays so that they appear to originate from a point on the same side as the object. Those rays never actually converge, so the image can only be formed by extending the rays backward, giving a virtual image.