Lecture Notes on Lens Construction and Focal Length

Introduction

Objective: To determine the relationship between the focal length of a lens and its various parameters, such as curvature and refractive index.
Lens Definition: A lens is a refracting medium bounded by at least one curved surface.
- Thin Lens: A lens is considered thin if its thickness is much smaller than the radius of curvature of its surfaces.

Principal Axis: The line passing through the center of the lens, known as the optic center.
Ray Diagrams: Used to determine where rays converge and thus identify the focal point.
- Parallel Ray: Passes through the optic center undeviated due to perpendicular incidence.
- Refracted Ray: Bends based on the normal at the point of incidence and the relative density of media.
Principal Focus: The point where initially parallel rays converge after passing through the lens.

Formula Components:
- Refracted Medium Index (Rm): Medium containing the refracted ray.
- Incident Medium Index (Im): Medium containing the incident ray.
- Image Distance (v), Object Distance (u), Radius of Curvature (R)
Multiple Surfaces: Apply the formula separately for each surface.
- Surface 1: Consider without the second surface.
- Surface 2: Apply after considering the effect of the first surface.

Virtual Object: The image formed by the first surface serves as the virtual object for the second surface.
Final Equation Derivation:
- Combine equations from both surfaces to eliminate the intermediate distance (v).
- Lens Maker's Equation: Derived from the combination, used to calculate focal length based on refractive indices and radii of curvature.

Lens Maker's Formula: Enables creation of lenses with specific focal lengths by adjusting refractive indices and curvatures.
General vs. Specific Cases: The formula applies generally without sign conventions. For specific numericals, sign conventions are used.
Applicability: The derived formula works for all types of thin lenses, whether convex or concave.

Understanding and applying the lens maker's equation is crucial for designing lenses with desired optical properties. It allows precise control over the lens's focal length by manipulating its physical parameters.