Ray Optics Class 12 Formulas: Mirrors, Lenses, Prism, Microscope and Telescope

Quick answer: Ray Optics is 6–8 marks in Class 12 boards, usually a derivation plus a numerical. Here is every formula with the sign convention that makes them work.

Sign convention

Distances from the pole/optical centre; along the incident light positive. Heights above the axis positive. Real object: u negative.

Mirrors and lenses

• Mirror: 1/v + 1/u = 1/f, m = −v/u, f = R/2
• Lens: 1/v − 1/u = 1/f, m = v/u, P = 1/f (D)
• Lens maker: 1/f = (n − 1)(1/R₁ − 1/R₂)
• Lenses in contact: 1/F = 1/f₁ + 1/f₂; P = P₁ + P₂
• Refraction at a spherical surface: n₂/v − n₁/u = (n₂ − n₁)/R

Refraction and TIR

• Snell: n₁ sin i = n₂ sin r; n = c/v = real depth/apparent depth
• Critical angle: sin C = 1/n; TIR when i > C (diamond, optical fibre, mirage)
• Lateral shift in a slab: d = t sin(i − r)/cos r

Prism

• i + e = A + δ; at minimum deviation r = A/2
• n = sin[(A + δ_m)/2] / sin(A/2)
• Thin prism: δ = (n − 1)A; dispersion because n depends on wavelength

Optical instruments

• Simple microscope: m = 1 + D/f (image at D), m = D/f (at infinity); D = 25 cm
• Compound microscope: m = (L/f_o)(1 + D/f_e) ≈ (L/f_o)(D/f_e)
• Telescope: m = f_o/f_e; length = f_o + f_e; large f_o for high magnification

Example

A convex lens n = 1.5 has R₁ = 10 cm, R₂ = −10 cm: 1/f = 0.5(1/10 + 1/10) = 0.1 → f = 10 cm. In water (n = 1.33) f becomes about 39 cm — lens gets weaker.

Common mistakes

• Using the lens sign convention for mirrors
• Forgetting R₂ is negative for a biconvex lens
• Using D = 25 cm as a variable instead of a constant

Related: Light Class 10 basics.

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Frequently asked questions

Are these Ray Optics Class 12 Formulas notes enough for the exam?

They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.

How should I revise Ray Optics Class 12 Formulas?

Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.

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