Class 12 · Chapter 9
Overview, notes, short notes, formula sheet, daily practice problems, previous year questions, and videos for this chapter — all in one place.
24 formulas across 5 topics in Ray Optics & Optical Instruments.
Updated 2026-07-09 · v1.0.0
Mirror formula and magnification apply identically to concave and convex mirrors once the sign convention is fixed — the formula never changes, only the signs of the quantities plugged in.
f = R/2
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| f | focal length | m | [L] |
| R | radius of curvature | m | [L] |
Valid when
1/v + 1/u = 1/f
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| v | image distance from the mirror | m | [L] |
| u | object distance from the mirror | m | [L] |
Valid when
Common mistakes
m = h'/h = −v/u
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| m | linear magnification | dimensionless | [M⁰L⁰T⁰] |
| h', h | image and object heights | m | [L] |
Valid when
P = 1/f (f in metres)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| P | power of the mirror | D (dioptre) | [L⁻¹] |
Valid when
xy = f²
Substituting u = −(f+x), v = −(f+y) into the mirror formula, where x, y are distances measured from the focus
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| x, y | object and image distances measured from the FOCUS (not the pole) | m | [L] |
Valid when
Light bends when crossing between media of different optical density — pushed far enough, it stops crossing at all and reflects entirely back, the basis of optical fibres.
n₁ sinθ₁ = n₂ sinθ₂ , n = c/v
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| n₁, n₂ | refractive indices of the two media | dimensionless | [M⁰L⁰T⁰] |
| θ₁, θ₂ | angles of incidence and refraction, measured from the normal | rad | [M⁰L⁰T⁰] |
Valid when
Apparent depth = Real depth / n
Small-angle approximation applied to Snell's law for near-normal viewing through a refracting surface
Valid when
Lateral shift = t sin(i−r) / cos r
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| t | thickness of the slab | m | [L] |
| i, r | angles of incidence and refraction at the first surface | rad | [M⁰L⁰T⁰] |
Valid when
sinθ(c) = 1/n (denser to rarer medium)
Setting θ₂ = 90° in Snell's law for light going from a denser medium (n) into a rarer one (n=1, e.g. air)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| θ(c) | critical angle | rad | [M⁰L⁰T⁰] |
Valid when
Common mistakes
n₂/v − n₁/u = (n₂ − n₁)/R
Applying Snell's law with paraxial (small-angle) approximation at a single curved boundary between two media
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| R | radius of curvature of the surface | m | [L] |
Valid when
The lens maker's formula ties a lens's focal length to its material and curvature; the lens formula then does the same job the mirror formula does for mirrors.
1/f = (n − 1)(1/R₁ − 1/R₂)
Applying refraction-at-a-single-surface twice in succession — once for each face of the thin lens
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| n | refractive index of the lens material relative to the surrounding medium | dimensionless | [M⁰L⁰T⁰] |
| R₁, R₂ | radii of curvature of the two lens surfaces (signed) | m | [L] |
Valid when
1/v − 1/u = 1/f
Valid when
Common mistakes
m = v/u
Valid when
P = 1/f (f in metres) ; P(combination) = P₁ + P₂ + ⋯
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| P | power of the lens | D (dioptre) | [L⁻¹] |
Valid when
1/F = 1/f₁ + 1/f₂ + ⋯
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| F | equivalent focal length of the combination | m | [L] |
Valid when
f = (d² − x²) / 4d
Two lens positions between a fixed object and screen both give a sharp image (conjugate foci property); combining the two equations gives this result
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| d | fixed distance between object and screen | m | [L] |
| x | distance between the two lens positions giving a sharp image | m | [L] |
Valid when
ω₁/f₁ + ω₂/f₂ = 0
Requires the net dispersive effect of both lenses to cancel while retaining some overall converging power
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| ω₁, ω₂ | dispersive powers of the two lens materials | dimensionless | [M⁰L⁰T⁰] |
Valid when
A prism bends light twice (once at each face); at one special angle of incidence the total deviation is minimised, and this minimum-deviation condition is how refractive index is measured experimentally.
n = sin[(A + δ(m))/2] / sin(A/2)
At minimum deviation, the ray path is symmetric inside the prism (i = e, r₁ = r₂ = A/2)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| A | angle of the prism | rad | [M⁰L⁰T⁰] |
| δ(m) | angle of minimum deviation | rad | [M⁰L⁰T⁰] |
Valid when
A = r₁ + r₂ , δ = i + e − A
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| i, e | angles of incidence and emergence | rad | [M⁰L⁰T⁰] |
| r₁, r₂ | angles of refraction at the two prism faces | rad | [M⁰L⁰T⁰] |
Valid when
ω = (n(v) − n(r)) / (n(y) − 1)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| n(v), n(r), n(y) | refractive indices for violet, red, and yellow (mean) light | dimensionless | [M⁰L⁰T⁰] |
Valid when
Microscopes and telescopes both use a two-lens system to magnify — a microscope magnifies a small NEARBY object, a telescope magnifies the apparent size of a distant one.
m = 1 + D/f (image at near point) ; m = D/f (image at infinity)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| D | least distance of distinct visionstandard value D = 25 cm | m | [L] |
| f | focal length of the magnifying lens | m | [L] |
Valid when
m ≈ (L/f(o)) × (D/f(e)) (image at near point, normal adjustment)
Product of the objective's linear magnification and the eyepiece's angular magnification (acting as a simple microscope on the intermediate image)
| Symbol | Meaning | Unit | Dimension |
|---|---|---|---|
| L | tube length — distance between the objective's image and the eyepiece's focal point (approx.) | m | [L] |
| f(o), f(e) | focal lengths of the objective and eyepiece | m | [L] |
Valid when
m = f(o)/f(e) (normal adjustment, image at infinity)
Ratio of the angles subtended by the final image and the object, using the objective's long focal length and the eyepiece's short one
Valid when
Common mistakes
Tube length (normal adjustment) = f(o) + f(e)
Valid when
Boards routinely ask for a labelled ray diagram alongside the magnification formula for both microscope and telescope — know the diagram, not just the number.
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