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Geometrical Optics Principles

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Snell's Law

The relationship between angles of incidence and refraction, when referring to wave propagation in different media:

n_1 \sin(\theta_1) = n_2 \sin(\theta_2)

Reflection Law

The angle of incidence is equal to the angle of reflection:

\theta_{incident} = \theta_{reflected}

Refraction

The bending of light as it passes from one medium to another with a different refractive index.

Critical Angle

The minimum angle of incidence for which total internal reflection occurs:

\theta_c = \arcsin(\frac{n_2}{n_1})

where

n_1 > n_2

Total Internal Reflection

A phenomenon where all the light incident on a boundary is reflected and none is refracted, occurring when the incident angle exceeds the critical angle.

Lens Formula

Describes the relationship between object distance $(d_o)$ , image distance $(d_i)$ , and the focal length $(f)$ of a lens:

\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}

Magnification

The ratio of the height of the image to the height of the object (or image distance to object distance in lens systems):

M = \frac{h_i}{h_o} = \frac{d_i}{d_o}

Focal Length of a Spherical Mirror

Half the radius of curvature $(R)$ for the mirror:

f = \frac{R}{2}

Fermat's Principle

The principle that states the path taken between two points by a ray of light is the path that can be traversed in the least time.

Ray Diagrams

A graphical method to predict the path of light and the image formation using simple geometric principles.

Optical Power

The degree to which a lens, mirror, or other optical system converges or diverges light, measured in diopters $(D)$ :

P = \frac{1}{f}

Mirror Equation

Relates object distance $(p)$ , image distance $(q)$ , and focal length $(f)$ for spherical mirrors:

\frac{1}{f} = \frac{1}{p} + \frac{1}{q}

Optical Path Length

The distance light travels in a medium, multiplied by the refractive index of the medium.

Thin Lens Approximation

Assumes the thickness of a lens is negligible compared to the object and image distances, simplifying calculations.

Converging Lens

A lens that bends light rays to a single focal point, having a positive focal length.

Diverging Lens

A lens that spreads out light rays, making them appear to originate from a single focal point behind the lens, with a negative focal length.

Real Image

An image that can be projected onto a screen as it is formed by the actual convergence of light rays.

Virtual Image

An image that cannot be projected onto a screen as it is formed by rays that appear to diverge from a common point.

Chromatic Aberration

The dispersion of light into its constituent colors due to differential refraction in lenses.

Spherical Aberration

An optical problem that occurs due to the spherical shape of lenses or mirrors, causing light rays to focus at different points.

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