Optics

The angle of incidence equals the angle of reflection, measured from the normal to the surface.

Relates focal length to object and image distances for spherical mirrors.

The ratio of image size to object size. Negative magnification indicates an inverted image.

The focal length of a spherical mirror is half its radius of curvature.

For light at normal incidence, the Fresnel equations simplify to give the reflection coefficient. R gives the fraction of intensity reflected.

The focal length of a spherical mirror is half the radius of curvature. This is the reciprocal form of f = R/2.

Describes how light bends when passing between media with different refractive indices.

The refractive index is the ratio of the speed of light in vacuum to its speed in the medium.

The angle of incidence above which total internal reflection occurs (when going from denser to less dense medium).

Objects in a denser medium appear closer to the surface due to refraction.

Relates the focal length of a thin lens to object and image distances. Same form as mirror equation.

Relates the focal length of a lens to its refractive index and surface curvatures.

Linear magnification of a thin lens. Negative values indicate inverted images.

The power of a lens in diopters is the reciprocal of focal length in meters.

For thin lenses in contact, the total power is the sum of individual powers.

Condition for constructive interference (bright fringes) in Young's double-slit experiment.

The spacing between adjacent bright (or dark) fringes in double-slit interference.

Condition for destructive interference (dark fringes) in single-slit diffraction. m = ±1, ±2, ...

Condition for principal maxima from a diffraction grating. Same form as double-slit but much sharper peaks.

The ability of a grating to distinguish between two closely spaced wavelengths.

Condition for constructive interference in thin films (when one reflection has phase shift). For destructive: 2nt = mλ.

The optical path length accounts for the change in wavelength when light travels through a medium. It equals the distance light would travel in vacuum in the same number of wavelengths.

Constructive interference occurs when the path difference between two waves is an integer multiple of the wavelength, resulting in maximum amplitude.

The angle of incidence at which reflected light is completely polarized.

The intensity of polarized light after passing through a polarizer at angle θ.

The minimum angular separation at which two point sources can be resolved by a circular aperture.

The angular magnification of a simple magnifying glass when the image is at the near point (25 cm). For relaxed viewing at infinity, M = D/f.

The total magnification of a compound microscope is the product of objective magnification (-L/f_o) and eyepiece magnification (D/f_e).

The angular magnification of an astronomical (refracting) telescope. The negative sign indicates an inverted image.

The numerical aperture characterizes the light-gathering ability and resolution of an optical system, particularly microscope objectives.

The f-number (or f-stop) is the ratio of focal length to aperture diameter. Lower f-numbers mean larger apertures and more light gathering.

Approximate depth of field for distant subjects. DOF increases with higher f-number (smaller aperture) and increases with the square of subject distance.

Angular dispersion describes how much the angle of refraction changes with wavelength. It depends on both the prism geometry and the material's dispersion.

At minimum deviation, light passes symmetrically through the prism. This formula relates the refractive index to the prism angle and minimum deviation.