Object 20 cm before a concave mirror of f = −15 cm. Find image.

1/v = 1/f − 1/u = −1/15 − 1/(−20) = −4/60 + 3/60 = −1/60 ⇒ v = −60 cm (real, inverted, magnified 3×).

A convex lens of f = 10 cm forms a virtual image 15 cm on the same side. Find object distance.

1/v − 1/u = 1/f ⇒ 1/(−15) − 1/u = 1/10 ⇒ 1/u = −1/15 − 1/10 = −1/6 ⇒ u = −6 cm.

Power of a lens is +2 D. What kind and focal length?

Positive → convex. f = 1/P = 0.5 m = 50 cm.

All Class 10 Science notes

Class 10 Science Notes — Chapter 9: Light — Reflection and Refraction

Reflection at curved surfaces, refraction through lenses, and sign convention.

Detailed NCERT notes

Light travels in straight lines; reflection follows i = r; incident ray, normal, reflected ray are coplanar.
Spherical mirrors: concave (converging), convex (diverging). Terms: pole P, centre of curvature C, radius R, principal axis, focus F, focal length f = R/2.
Image formation by concave mirror depends on object position (at infinity, beyond C, at C, between C & F, at F, between F & P). Practise the six cases.
Convex mirror always produces virtual, erect, diminished image between P and F.
Mirror formula: 1/v + 1/u = 1/f. Magnification m = −v/u = h'/h.
Refraction: bending of light on going from one medium to another due to change in speed.
Laws: incident ray, refracted ray, normal are coplanar; sin i / sin r = constant = ₁n₂ (Snell's law).
Refractive index n = c/v (c in vacuum, v in medium); denser medium ⇒ higher n; light slows and bends toward normal.
Lens: converging (convex) or diverging (concave). Focal length by convention: convex positive, concave negative.
Lens formula: 1/v − 1/u = 1/f. Magnification m = v/u = h'/h.
Power of a lens P = 1/f (with f in metres). Unit: dioptre (D). Combined power = P₁ + P₂ + ...
New Cartesian sign convention: pole/optical centre is origin; incident light travels along +x direction; heights above principal axis are positive.
Image characteristics table:
Concave mirror: real & inverted (u beyond F); virtual & erect & magnified (u < F).
Convex mirror: always virtual, erect, diminished.
Convex lens: real & inverted for u > f; virtual & erect & magnified for u < f (magnifying glass).
Concave lens: always virtual, erect, diminished.

Formulas & key results

Mirror formula: 1/v + 1/u = 1/f; m = −v/u
Lens formula: 1/v − 1/u = 1/f; m = v/u
Snell: n₁ sin i = n₂ sin r; n = c/v
Power P = 1/f (f in metres); unit: dioptre
f = R/2

Mind map

Reflection (plane, spherical) → refraction → lenses
Sign convention
Image formation cases
Power of lens

Tricks & shortcuts

New Cartesian: distances from pole, along incident light → +; opposite → −.
m > 0 → erect virtual; m < 0 → inverted real (mirrors).

Common mistakes to avoid

Sign errors — especially for concave mirror/lens.
Interchanging u and v.
Using degrees vs radians in Snell (they don't matter individually — but consistency does).

Competency-based questions & answers

Q. Object 20 cm before a concave mirror of f = −15 cm. Find image.
A. 1/v = 1/f − 1/u = −1/15 − 1/(−20) = −4/60 + 3/60 = −1/60 ⇒ v = −60 cm (real, inverted, magnified 3×).
Q. A convex lens of f = 10 cm forms a virtual image 15 cm on the same side. Find object distance.
A. 1/v − 1/u = 1/f ⇒ 1/(−15) − 1/u = 1/10 ⇒ 1/u = −1/15 − 1/10 = −1/6 ⇒ u = −6 cm.
Q. Power of a lens is +2 D. What kind and focal length?
A. Positive → convex. f = 1/P = 0.5 m = 50 cm.