Spherical Mirrors

• Concave and convex spherical mirrors — pole (P), centre of curvature (C), radius (R), principal axis, focus (F).
• Sign convention (NCERT): object distance u negative; distances along incident light positive.
• Mirror formula: 1/f = 1/v + 1/u; focal length f = R/2.
• Image types — real/inverted (concave, object beyond F) vs virtual/erect (concave within F; convex always).
• Uses: shaving mirror (concave), rear-view mirror (convex), dentist's mirror, solar furnaces.

1. Concave mirror — reflecting surface curved inward; converges parallel rays to real focus F.
2. Convex mirror — surface curved outward; diverges rays; virtual focus behind mirror.
3. Sign convention — u always negative for real object; v negative for real image in front; f negative for concave, positive for convex.
4. Mirror formula — 1/f = 1/v + 1/u (valid for paraxial rays).
5. Magnification — m = h'/h = −v/u; |m| > 1 enlarged, |m| < 1 diminished.
6. Concave uses — torch reflector, shaving mirror, dentist mirror, solar cooker.
7. Convex uses — rear-view mirror (wide field, diminished image), shop security mirror.
8. Real image — can be obtained on screen; formed by concave when object beyond F.
9. Diagram (text) — object at 2F of concave → image at 2F, same size, inverted, real.
10. NCERT Activity — locate image by ray diagram for object at C, between C and F, at F.

Image of object 30 cm from concave mirror (f = 15 cm)

Given: u = −30 cm, f = −15 cm (concave)
Step 1 — Mirror formula: 1/f = 1/v + 1/u
Step 2 — 1/(−15) = 1/v + 1/(−30)
Step 3 — 1/v = −1/15 + 1/30 = −1/30 → v = −30 cm
Step 4 — v negative → real image 30 cm in front of mirror
Step 5 — m = −v/u = −(−30)/(−30) = −1 → same size, inverted
Conclusion: object at 2F gives image at 2F (NCERT standard case).

• Using 1/f = 1/v − 1/u (lens sign) instead of mirror formula 1/f = 1/v + 1/u.
• Forgetting u is negative for real object in NCERT sign convention.
• Assuming convex mirror gives real image (always virtual, erect, diminished).
• Confusing R and f — f = R/2, not 2R.
• Measuring distances from mirror surface instead of pole P.

• State mirror formula with sign convention for u and f (concave).
• Why is convex mirror used as rear-view mirror?
• Where is image when object is at focus F of concave mirror?
• If f = −10 cm and u = −25 cm, is image real or virtual?

Open the Practice tab for graded questions on Spherical Mirrors.