Mirror formula: 1/v + 1/u = 1/f (sign convention: Cartesian).

Magnification: m = –v/u = h'/h.

Concave mirror: f = –R/2 (real focus), Convex mirror: f = +R/2 (virtual focus).

Lens maker formula: 1/f = (n – 1)(1/R₁ – 1/R₂)

Lens formula: 1/v – 1/u = 1/f (sign convention).

Power: P = 1/f (in m) → Dioptre (D).

Prism formula: δ = i₁ + i₂ – A (angle of deviation).
At minimum deviation: i₁ = i₂, r₁ = r₂ = A/2, n = sin[(A+δ_m)/2] / sin(A/2).

Simple microscope: Angular magnification m = 1 + D/f (when image at near point).

Compound microscope: m = m_o × m_e = (v_o/u_o) × (1 + D/f_e).
For image at infinity: m = (L × D)/(f_o f_e) where L = tube length.

Astronomical telescope (normal adjustment): m = f_o/f_e, length L = f_o + f_e.
When image at near point: m = f_o/f_e (1 + f_e/D).

Resolving power: R = 1/θ = a/(1.22λ) for telescope.

💡 NEET TIPS & SHORTCUTS

• Sign convention (Cartesian): object distance u always negative; f negative for concave mirror & convex lens? Wait: for lens, convex lens has +f, concave lens –f. For mirror, concave –f, convex +f.
• For a prism, δ_min depends on n and A; for small A, δ = (n–1)A.
• Resolving power of microscope = 2n sinθ/λ; of telescope = a/(1.22λ).

⚠️ COMMON MISTAKES

• Confusing sign conventions between mirrors and lenses.
• Using lens formula 1/v – 1/u = 1/f incorrectly (check sign of u).
• Forgetting that total internal reflection requires n₁ > n₂.
• In compound microscope, tube length = v_o + u_e.

Mirror formula: 1/v + 1/u = 1/f

Lens formula: 1/v – 1/u = 1/f

Snell's law: n₁ sin i = n₂ sin r

Lens maker: 1/f = (n–1)(1/R₁ – 1/R₂)

Microscope magnification: m = (v_o/u_o) × (1 + D/f_e)

Telescope magnification: m = f_o/f_e