Important Terms & Key Relation
Definitions
R = 2fRadius of curvature = twice the focal length
New Cartesian Sign Convention
Rules (NCERT / CBSE)
Origin at Pole (mirrors) or Optical Centre O (lenses).
Direction of incident light (left → right) = positive.
Distances opposite to incident light = negative.
Heights above principal axis = +ve; below = −ve.
Object always on left → u always negative.
Concave mirror: F & C on left → f < 0. Convex mirror → f > 0.
Convex lens: f > 0. Concave lens: f < 0.
Laws of Reflection (NCERT exact wording)
"The angle of incidence is equal to the angle of reflection."
"The incident ray, the reflected ray and the normal to the mirror at the point of incidence all lie in the same plane."
Image Formation by Mirrors
Concave Mirror — NCERT Table 9.1
| Position of Object | Position of Image | Size of Image | Nature of Image |
|---|---|---|---|
| At infinity | At focus F | Highly diminished, point-sized | Real & inverted |
| Beyond C | Between F and C | Diminished | Real & inverted |
| At C | At C | Same size | Real & inverted |
| Between C and F | Beyond C | Enlarged | Real & inverted |
| At F | At infinity | Image would not be formed | Image would not be formed |
| Between P and F | Behind the mirror | Enlarged | Virtual & erect |
NCERT Note: "Image would not be formed" is the exact textbook phrasing — the image travels to infinity and cannot be collected on a screen.
Sign Table — Concave Mirror (f < 0)
| Object Position | Image Position | u | v | h₀ | hᵢ |
|---|---|---|---|---|---|
| At infinity | At F | − | − | + | − |
| Beyond C | Between C & F | − | − | + | − |
| At C | At C | − | − | + | − |
| Between C & F | Beyond C | − | − | + | − |
| At F | At infinity | − | − | + | − |
| Between F & P | Behind mirror | − | + | + | + |
- u always negative — object placed to the left.
- Real image →
v negative; image height negative (inverted). - Virtual image (between F & P) →
v positive; image height positive (erect).
Convex Mirror — Image Formation
| Position of Object | Position of Image | Size | Nature |
|---|---|---|---|
| At infinity | At F (behind mirror) | Highly diminished | Virtual & erect |
| Anywhere (finite) | Between P & F | Diminished | Virtual & erect |
| SIGN TABLE — CONVEX MIRROR (f > 0) | |||||
|---|---|---|---|---|---|
| Object Position | Image Position | u | v | h₀ | hᵢ |
| At infinity | At F (behind mirror) | − | + | + | + |
| Anywhere | Between P & F | − | + | + | + |
Mirror Formula & Magnification
1/f = 1/v + 1/um = hᵢ / h₀ = −v / u- m < 0 → inverted (real image). m > 0 → erect (virtual image).
- |m| > 1 → magnified · |m| < 1 → diminished · |m| = 1 → same size.
Refraction & Refractive Index
Definition
Refraction is the change in direction of light when it passes from one transparent medium to another due to a change in its speed.
Laws of Refraction (NCERT exact wording)
"The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane."
"The ratio of sine of angle of incidence to the sine of angle of refraction is constant for a given pair of media — sin i / sin r = constant."
n = sin i / sin rn = c / vc = speed of light in vacuum
Glass Slab — Key Facts
- Emergent ray is parallel to the incident ray (net deviation = 0°).
- Lateral displacement depends on slab thickness, angle of incidence, and refractive index.
- Lateral displacement:
d = t × sin(i − r) / cos r
Image Formation by Lenses
- Convex lens (converging) — f > 0, P > 0.
- Concave lens (diverging) — f < 0, P < 0.
Convex Lens — NCERT Table 9.4
| Position of Object | Position of Image | Relative Size | Nature |
|---|---|---|---|
| At infinity | At focus F₂ | Highly diminished, point-sized | Real & inverted |
| Beyond 2F₁ | Between F₂ & 2F₂ | Diminished | Real & inverted |
| At 2F₁ | At 2F₂ | Same size | Real & inverted |
| Between F₁ & 2F₁ | Beyond 2F₂ | Enlarged | Real & inverted |
| At focus F₁ | At infinity | Image would not be formed | Image would not be formed |
| Between F₁ & O | Same side as object | Enlarged | Virtual & erect |
| SIGN TABLE — CONVEX LENS (f > 0) | |||||
|---|---|---|---|---|---|
| Object Position | Image Position | u | v | h₀ | hᵢ |
| At infinity | At F₂ | − | + | + | − |
| Beyond 2F₁ | Between F₂ & 2F₂ | − | + | + | − |
| At 2F₁ | At 2F₂ | − | + | + | − |
| Between F₁ & 2F₁ | Beyond 2F₂ | − | + | + | − |
| At F₁ | At infinity | − | + | + | − |
| Between F₁ & O | Same side (virtual) | − | − | + | + |
Concave Lens — Image Formation
| Position of Object | Position of Image | Size | Nature |
|---|---|---|---|
| At infinity | At F (same side) | Highly diminished | Virtual & erect |
| Anywhere (finite) | Between O & F | Diminished | Virtual & erect |
| SIGN TABLE — CONCAVE LENS (f < 0) | |||||
|---|---|---|---|---|---|
| Object Position | Image Position | u | v | h₀ | hᵢ |
| At infinity | At F | − | − | + | + |
| Anywhere | Between O & F | − | − | + | + |
- Real image by lens →
v positive. Virtual image →v negative. - Concave lens always forms a virtual, erect, diminished image on the same side as the object.
Lens Formula, Magnification & Power
1/f = 1/v − 1/uMinus sign — different from mirror!
m = hᵢ / h₀ = v / uNo negative sign — different from mirror
P = 1 / f (f in metres)Unit: Dioptre (D)
Convex: P > 0 · Concave: P < 0
Compact Cheat Table
| Type | f sign | Real image v sign | Virtual image v sign |
|---|---|---|---|
| Concave Mirror | − | − | + |
| Convex Mirror | + | n/a — no real image | + |
| Convex Lens | + | + | − |
| Concave Lens | − | n/a — no real image | − |
Must-Remember Lines & Ray Diagram Steps
NCERT / Exemplar — Copy Into Answers
Ray Diagram Steps (exam style)
Concave Mirror — Object Beyond C
Ray parallel to axis — reflects through F.
Ray through C — reflects back on itself.
Ray through F — reflects parallel to axis.
Convex Lens — Object Between F₁ & O
Ray parallel to axis — refracts through F₂.
Ray through O — passes undeviated.
Ray through F₁ — emerges parallel to axis.
7 Important Worked Numericals
All arithmetic rechecked digit-by-digit. Write steps in this exact format for boards.
Concave mirror · m = −1, image on screen at 50 cm
u = −50 cmf = −25 cm50 cmConcave mirror · u = −20 cm, v = −30 cm — find f
Convex lens · u = −30 cm, v = +60 cm — find f
Power of lens · f = 25 cm
0.25 m4 DConcave mirror · u = −10 cm, v = −30 cm, h₀ = 2.0 cm
−3−6 cmGlass slab · t = 4.0 cm, μ = 1.50, i = 30° — lateral displacement
1/3Convex lens · f = 20 cm, u = −30 cm, h₀ = 4 cm
v = +60 cm−2−8 cmBoard Exam Tips & Checklist
Write origin, u sign, and f sign before any calculation.
Write the formula before substituting — earns method marks.
Use cm for optics; convert to m for Power and show the step.
Label P, C, F (mirrors) and O, F₁, F₂ (lenses).
Real/virtual; erect/inverted; magnified/diminished — always.
Mirror: m = −v/u · Lens: m = v/u — never mix these.
Always start: "Emergent ray is parallel to incident ray."
Real image → v negative. Virtual → v positive.
Definitions 1–2 min · Diagram 3–4 min · Numerical 5–8 min.
Box the final answer, include units, add one-line nature statement.