CBSE Class 12 Physics: Ray Optics — Mirrors, Lenses & Notes 2026

Reflection from Curved Surfaces

• Mirror formula: 1/v + 1/u = 1/f; f = R/2; sign convention: distances from pole
• Magnification m = −v/u; real inverted negative; virtual erect positive
• Focal length independent of medium (unlike lenses)

Refraction and Snell's Law

• n = c/v; n₁ sin i = n₂ sin r (Snell's law)
• Critical angle C: sin C = n₂/n₁ (for n₁ > n₂); TIR when i > C
• Applications of TIR: optical fibres, diamonds, mirages, periscopes

Refraction at Spherical Surface

• n₂/v − n₁/u = (n₂−n₁)/R; derive using geometry and small angle approximation
• Lensmaker's equation: 1/f = (n−1)[1/R₁ − 1/R₂]; lens in medium
• Thin lens formula: 1/v − 1/u = 1/f; magnification m = v/u

Prism and Dispersion

• Deviation δ = (i₁ + i₂) − A; minimum deviation D_m when i₁ = i₂
• n = sin[(A+D_m)/2] / sin(A/2)
• Dispersion: different colours have different refractive indices; violet deviates most

Optical Instruments — Microscope

• Simple microscope: m = D/f (at near point) or m = 1 + D/f (image at infinity)
• Compound microscope: m = m_e × m_o = (L/f_o) × (D/f_e); L = tube length
• Resolving power: ability to distinguish two close objects; increases with NA

Optical Instruments — Telescope

• Refracting telescope magnification m = f_o/f_e (image at infinity)
• Reflecting telescope: uses concave mirror (no chromatic aberration, larger aperture)
• Astronomical vs. terrestrial telescope: additional erecting lens in terrestrial

CBSE Exam — Ray Optics

• Derive lens maker's equation
• A prism of angle 60° and n=1.5; find minimum deviation
• Numerical: microscope with given f_o and f_e, tube length; find total magnification