Geometric Optics

Reflection & Mirrors - Light's Mirror Magic

• Laws of Reflection:
  • Angle of incidence $i = r$.
  • Incident ray, reflected ray, normal are coplanar.
• Plane Mirror:
  • Image: Virtual, erect, same size, laterally inverted. $m = +1$, $f = \infty$.

  ⭐ Image formed by a plane mirror is virtual, erect, laterally inverted, and same size as the object.

• Spherical Mirrors: (Concave/Converging, Convex/Diverging)
  • Mirror Formula: $1/f = 1/v + 1/u$. (Use New Cartesian Sign Convention).
  • Focal length: $f = R/2$ (R: Radius of Curvature).
  • Magnification: $m = -v/u = h_i/h_o$ ($h_i$: image height, $h_o$: object height).
• Concave (Converging): Image varies (real/virtual, inverted/erect). E.g., Ophthalmoscope, head mirror.
• Convex (Diverging): Image always virtual, erect, diminished. E.g., Rear-view mirrors (wider field of view).

Refraction & Prisms - Light Bends Here

• Refraction: Light bends at interface.
  • Snell's Law: $n_1 \sin \theta_1 = n_2 \sin \theta_2$.
  • RI $n = c/v$. 📌 RIde a BIke (Rarer→Denser, Bends Towards normal).
  • Critical Angle $C$: Incidence in denser medium for 90° refraction. $ \sin C = n_2/n_1 $ (where $n_1$ is denser).
  • TIR: Incidence > $C$ (denser→rarer).
• Prisms: Deviate light to base; disperse.
  • Apical angle $A$. Min. deviation $D_m$: $\mu = \sin((A+D_m)/2) / \sin(A/2)$.
  • Power: Prism Diopter ($\Delta$); 1$\Delta$ = 1cm dev. at 1m.

⭐ TIR is key for optical fibers, gonioscopy, and some ophthalmic lenses.

Lenses & Formulas - Focusing on Vision

• Lenses alter light paths. Power in Diopters (D).
• Types:
  • Convex (Converging): Positive power.
  • Concave (Diverging): Negative power. 📌 CIVIL (Concave lens Image Virtual, Erect, Diminished, In front of lens).

• Key Formulas:
  • Lens Maker's: $1/f = (\mu-1)(1/R_1 - 1/R_2)$
  • Thin Lens: $1/f = 1/v - 1/u$
  • Power: $P = 1/f$ (f in m)

Image Formation by Lenses:

Image Formation by Convex Lens (Object Position):

Eye's Optics & Aberrations - Vision's Imperfections

• Total eye power: +58D to +60D. Cornea: +43D; Lens: +15D to +20D (variable with accommodation).
• Axial length (emmetropia): approx. 24mm.
• Reduced Eye Model: Simplification with single refracting surface (approx. +60D).
• Aberrations: Imperfections degrading retinal image quality.
  • Spherical: Peripheral rays focus more anteriorly than paraxial rays. Minimized by pupil constriction. Cornea's aspheric shape (flatter periphery) naturally reduces this.
  • Chromatic: Different wavelengths (colors) focus at different points. Shorter wavelengths (blue) refract more strongly than longer wavelengths (red).
    • Principle behind duochrome test.
  • Other (often higher-order): Coma, oblique astigmatism, field curvature, distortion.

⭐ The cornea contributes approximately two-thirds of the eye's total refractive power.

High‑Yield Points - ⚡ Biggest Takeaways

• Snell's Law: Governs light bending at media interfaces via refractive index.
• Lens Power (D): Reciprocal of focal length (m). Convex (+) converge, concave (-) diverge.
• Prisms: Deviate light to base. Power in PD. Prentice's rule: PD from decentration (cm) and lens power (D).
• Refractive Errors: Myopia (concave lens), Hyperopia (convex lens), Astigmatism (cylindrical lens).
• Pinhole Test: Improves vision in refractive error by ↑ depth of focus, differentiates from pathology.
• Sturm's Conoid: Interval of Sturm in astigmatism due to two focal lines.