Ray Optics

Concept overview

Ray optics treats light as straight-line rays that reflect off mirrors and refract through interfaces. Reflection obeys θᵢ = θᵣ. Refraction obeys Snell's law: n₁ sin θ₁ = n₂ sin θ₂, where n = c/v is the refractive index of a medium.

The mirror formula 1/v + 1/u = 1/f connects object distance u, image distance v and focal length f. For a spherical mirror f = R/2. The Cartesian sign convention — distances measured from the pole, with the incident direction taken as positive — is essential; a wrong sign gives a wrong image location.

For a thin lens, the lens maker's equation is 1/f = (n − 1)(1/R₁ − 1/R₂). The thin-lens equation 1/v − 1/u = 1/f is used for image formation. Magnification m = v/u for lenses, and m = −v/u for mirrors.

Total internal reflection occurs when light in a denser medium hits the interface with a less dense medium at an angle exceeding the critical angle θ_c = sin⁻¹(1/n). This is the basis of optical fibres. Prisms disperse light because refractive index depends on wavelength; angle of deviation δ = i₁ + i₂ − A, minimising when i₁ = i₂ giving δ_min and A_prism related to n.

Key formulas & concepts

• Snell's law: n₁ sin θ₁ = n₂ sin θ₂
• Mirror formula: 1/v + 1/u = 1/f; f = R/2
• Thin lens equation: 1/v − 1/u = 1/f
• Lens maker's equation: 1/f = (n − 1)(1/R₁ − 1/R₂)
• Magnification (lens): m = v/u
• Critical angle: sin θ_c = 1/n (for TIR at interface)
• Prism minimum deviation: n = sin((A + δ_min)/2) / sin(A/2)
• Power of lens: P = 1/f (in metres); units: dioptre

Common mistakes to avoid

• Using cm for f but m for u — always work in consistent units.
• Forgetting the sign convention — real objects have negative u; real images have positive v; concave mirrors and convex lenses have positive f.
• Applying the small-angle Snell approximation when angles are actually large.
• Confusing lateral magnification with angular magnification — they mean different things for microscopes and telescopes.

JEE Main relevance

JEE Main asks 2 ray-optics problems every paper — usually one mirror/lens image-formation and one Snell's law or prism problem. Small formula set, high recurrence.

JEE Advanced relevance

Advanced problems combine multiple optical elements — a lens plus a mirror, or a lens system with an intermediate object. Optical instrument design (microscope, telescope) also appears at the Advanced level.

Previous-year questions (PYQ)

Lens and mirror image-formation PYQs are the most repeated single archetype. Drill 20 of them in a chapter-wise session.