Ray Optics and Optical Instruments Class 12 Notes (2026-27) — CBSE
Class 12 Physics Chapter 9 notes: mirrors, refraction, total internal reflection, lens maker's formula, prisms, and microscopes and telescopes.
Ray Optics and Optical Instruments — Class 12 Physics Notes
Chapter Snapshot
This chapter treats light as rays and works out where images form. It covers spherical mirrors, refraction and total internal reflection, refraction at spherical surfaces leading to the lens maker's formula, prisms and minimum deviation, and finally optical instruments — the microscope and telescope.
Board relevance: Optics (with Chapter 10) is one of the biggest units, ~10 marks. Expect a lens or prism numerical and an optical-instrument derivation. The sign convention decides whether your answer is right.
Key Concepts & Definitions
Sign convention (New Cartesian): distances are measured from the pole/optical centre; those along the incident light are positive, against it negative. So the object distance u is always negative. Heights above the axis are positive.
Mirror formula and magnification:
1/v + 1/u = 1/f , m = −v/u = h'/h , f = R/2
Concave mirror f is negative, convex positive. Negative m ⇒ real, inverted image.
Refraction — Snell's law:
n₁ sin i = n₂ sin r , or n₂₁ = sin i/sin r = v₁/v₂
Absolute refractive index n = c/v. Light bends towards the normal entering a denser medium.
Real and apparent depth: an object under water appears raised. n = real depth / apparent depth.
Total Internal Reflection
When light goes from a denser to a rarer medium and the angle of incidence exceeds the critical angle C, it is completely reflected back.
sin C = 1/n (n = refractive index of denser w.r.t. rarer)
Two conditions: (1) denser → rarer, (2) i C.
Applications: optical fibres (signal travels by repeated TIR), sparkle of diamonds (very small C ≈ 24°), mirage, and totally reflecting prisms in periscopes and binoculars.
Formulas — Spherical Surfaces and Lenses
Refraction at a single spherical surface:
n₂/v − n₁/u = (n₂ − n₁)/R
Lens maker's formula:
1/f = (n − 1)(1/R₁ − 1/R₂)
Thin lens formula and magnification:
1/v − 1/u = 1/f , m = v/u = h'/h
Power of a lens: P = 1/f (f in metres), unit dioptre (D). Convex lens: f and P positive; concave: negative.
Lenses in contact:
1/f = 1/f₁ + 1/f₂ + … , P = P₁ + P₂ + …
Prism
For a prism of angle A, with incidence i, emergence e, refraction angles r₁, r₂ and deviation δ:
A + δ = i + e and r₁ + r₂ = A
At minimum deviation δm, the ray passes symmetrically (i = e, r₁ = r₂ = A/2):
n = sin[(A + δm)/2] / sin(A/2)
The δ–i graph is a curve with a single minimum at δm.
Optical Instruments
Simple microscope (magnifying glass) — a single convex lens of short focal length:
- Image at near point: m = 1 + D/f
- Image at infinity (relaxed eye): m = D/f (D = 25 cm, least distance of distinct vision)
Compound microscope — objective (small fo) + eyepiece (small fe):
- m = mo × me = (vo/uo)(1 + D/fe), or approximately m ≈ (L/fo)(D/fe) for a long tube.
- Both focal lengths are made small for high magnification.
Astronomical telescope — objective (large fo) + eyepiece (small fe):
- Relaxed eye: m = fo/fe, tube length L = fo + fe.
- A large objective aperture gathers more light and improves resolution.
Worked Examples
Example 1 — Critical angle: Find the critical angle for glass of refractive index 1.5.
sin C = 1/n = 1/1.5 = 0.667 → C ≈ 41.8°.
Example 2 — Lens maker's formula: A double convex lens (n = 1.5) has R₁ = 20 cm, R₂ = −20 cm. Find f.
1/f = (1.5 − 1)(1/20 − 1/(−20)) = 0.5(1/20 + 1/20) = 0.5(2/20) = 1/20 → f = 20 cm (converging).
Example 3 — Prism: A prism of angle 60° has δm = 30°. Find its refractive index.
n = sin[(60 + 30)/2]/sin(60/2) = sin 45°/sin 30° = 0.707/0.5 = 1.414 (≈ √2).
Example 4 — Telescope: A telescope has fo = 100 cm and fe = 5 cm. Find the magnifying power and tube length.
m = fo/fe = 100/5 = 20; L = 100 + 5 = 105 cm.
Important Question Patterns
1. Mirror/lens numerical (3 marks): apply 1/v + 1/u = 1/f (mirror) or 1/v − 1/u = 1/f (lens) with the sign convention; find magnification and image nature.
2. Total internal reflection (2–3 marks): conditions; sin C = 1/n; explain optical fibres or the sparkle of a diamond.
3. Lens maker's / power (2–3 marks): compute f from R₁, R₂ and n; power and combinations of lenses in contact.
4. Prism (3 marks): A + δ = i + e; the minimum-deviation formula; find n or δm.
5. Optical instruments (3–5 marks): derive/state magnifying power of the compound microscope or telescope; why the objective of a telescope has a large aperture and long focal length.
⚡ Quick Revision
- Sign convention: measure from pole/optical centre; u always negative. Mirror 1/v + 1/u = 1/f, m = −v/u; f = R/2. Lens 1/v − 1/u = 1/f, m = v/u.
- Snell: n₁ sin i = n₂ sin r; n = c/v; n = real depth/apparent depth.
- TIR: denser → rarer and i C, where sin C = 1/n. Uses: optical fibre, diamond, mirage, prisms in binoculars.
- Spherical surface: n₂/v − n₁/u = (n₂ − n₁)/R. Lens maker: 1/f = (n − 1)(1/R₁ − 1/R₂).
- Power P = 1/f (m), dioptre; in contact P = P₁ + P₂.
- Prism: A + δ = i + e, r₁ + r₂ = A; n = sin[(A + δm)/2]/sin(A/2).
- Simple microscope: m = 1 + D/f (near point), D/f (infinity), D = 25 cm.
- Compound microscope: m ≈ (L/fo)(D/fe) — both f small. Telescope: m = fo/fe, L = fo + fe — large fo, small fe.
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