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Ray Optics and Optical Instruments

NCERT Class 12 Physics Chapter 9

Ray Optics and Optical Instruments for Class 12 Physics, JEE and NEET: mirrors, refraction, total internal reflection, lenses, prisms and instruments.

9 topics Updated 8 Nov 2026

For: Class 12, JEE and NEET, unless a topic says otherwise

In the syllabus: JEE Class 12 syllabus, NEET Class 12 syllabus

With your textbook

NCERT Physics Part II (Class 12), Chapter 9 “Ray Optics and Optical Instruments”, reprint 2026-27.

Open the official NCERT chapter (PDF, 3.4 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Reflection of light by spherical mirrors

    Spherical mirrors, sign convention, f = R/2, derivation of 1/v + 1/u = 1/f, magnification, solved examples.

    NCERT Section 9.2 16 min read 4 solved examples 7 practice questions

  2. Refraction

    Snell’s law, refractive index and optical density, lateral shift through a slab, real and apparent depth.

    NCERT Section 9.3 13 min read 4 solved examples 7 practice questions

  3. Experiment: refractive index of a glass slab with a travelling microscope

    Travelling microscope method, n = (a − a)/(a − a), least count, errors and precautions.

    JEE and NEET only 12 min read 4 solved examples 8 practice questions

  4. Total internal reflection

    Its two conditions, the critical angle formula, totally reflecting prisms and optical fibres.

    NCERT Section 9.4 13 min read 4 solved examples 7 practice questions

  5. Refraction at spherical surfaces and by lenses

    Refraction at a curved surface, thin lens formula 1/v − 1/u = 1/f, magnification, power, combinations.

    NCERT Section 9.5 18 min read 5 solved examples 7 practice questions

  6. Experiment: focal length of mirrors and a lens by the parallax method

    Parallax method, index correction, f = uv/(u + v), 1/u–1/v graph, examples.

    JEE and NEET only 14 min read 4 solved examples 7 practice questions

  7. Refraction through a prism

    Refraction through a prism, δ = i + e − A, prism formula n = sin[(A + Dm)/2]/sin(A/2), thin prism.

    NCERT Section 9.6 11 min read 4 solved examples 9 practice questions

  8. Experiment: angle of deviation against angle of incidence for a prism

    Tracing rays with pins, the i–δ graph, reading the angle of minimum deviation and finding the refractive index.

    JEE and NEET only 12 min read 4 solved examples 7 practice questions

  9. Optical instruments: microscopes and telescopes

    Simple microscope, refracting and Cassegrain telescopes, magnifying power formulas, examples.

    NCERT Section 9.7 18 min read 4 solved examples 7 practice questions

Key formulas in this chapter

Spherical mirrors

  • f = R/2
  • 1/v + 1/u = 1/f
  • m = h′/h = −v/u

Refraction

  • sin i/sin r = n21
  • n1 sin i = n2 sin r
  • n12 = 1/n21
  • n32 = n31 × n12
  • apparent depth h1 = h2/n
  • shift through a slab = t(1 − 1/n)

Experiment: glass slab

  • n = real thickness/apparent thickness
  • n = (a3 − a1)/(a3 − a2)
  • rise of the mark = t(1 − 1/n)
  • Δn/n = Δb/b + Δc/c

Total internal reflection

  • sin ic = n21
  • in air: sin ic = 1/n

Lenses

  • n2/v − n1/u = (n2 − n1)/R
  • 1/f = (n21 − 1)(1/R1 − 1/R2)
  • 1/v − 1/u = 1/f
  • m = h′/h = v/u
  • P = 1/f
  • 1/f = 1/f1 + 1/f2 + 1/f3 + …
  • P = P1 + P2 + P3 + …
  • m = m1 m2 m3 …

Experiment: focal lengths

  • f = uv/(u + v)
  • convex mirror: f = R/2 = PC/2
  • Δf/f2 = Δu/u2 + Δv/v2

Prism

  • r1 + r2 = A
  • δ = i + e − A
  • r = A/2, i = (A + Dm)/2
  • n21 = sin[(A + Dm)/2]/sin(A/2)
  • Dm ≈ (n21 − 1)A

Experiment: prism i–δ graph

  • δ = i + e − A
  • n = sin[(A + Dm)/2]/sin(A/2)

Optical instruments

  • m = 1 + D/f
  • m = D/f
  • mo = L/fo
  • m = (L/fo)(D/fe)
  • m ≈ (L/fo)(1 + D/fe)
  • m = fo/fe
  • m = (fo/fe)(1 + fe/D)

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