1 Optics
Properties of Light
Light behaves both as waves and as particles (photons)
Its speed (velocity) (v) is directly proportional to wavelength (λ) and frequency (ν): v = λν
Index of refraction (n)
ratio of speed of light in a vacuum to speed of light in specific material (n = c/v)
Coherence
ability of 2 light beams to cause interference (large white source has a coherence close to zero)
Scattering
disruption of light by irregularities in light path; shorter wavelengths scatter to a greater extent
Refraction
Snell’s law
n sin (i) = n′ sin (r); n = refractive index of material; i = angle of incidence (measured from the normal); r = angle of refraction (measured from the normal) (Figure 1-2)
Critical angle
Example: Glass / air interface has a critical angle of 41°; critical angle of cornea = 46.5°
Prisms
Prisms displace and deviate light (because their surfaces are nonparallel); light rays are deviated toward the base; image is displaced toward the apex (Figure 1-3)
Prism diopter (PD, Δ)
displacement (in cm) of light ray passing through a prism, measured 100 cm (1 m) from prism
Angle of minimum deviation
total angle of deviation is least when there is equal bending at both surfaces of prism
Plastic prisms are calibrated by angle of minimum deviation: back surface parallel to frontal plane
Glass prisms are calibrated in Prentice position: back surface perpendicular to visual axis
Prism placed in front of the eye creates a phoria in the direction of the base
Stacking prisms is not additive; 1 prism in front of each eye is additive
Prismatic effect of lenses (Figure 1-4)
Figure 1-4 A, Plus lenses act like 2 prisms base to base. B, Minus lenses act like 2 prisms apex to apex.
Perceived movement of fixation target when lens moves in front of the eye:
Prentice’s rule
Example: Reading 1 cm below optical center: OD − 3.00; OS + 1.00 + 3.00 × 90
OD (Oculus Dexter – right eye): prism power = 1 cm × 3 D = 3 Δ BD
Net prismatic effect = 4 Δ (either BD over OD, or BU over OS)
Prismatic effect of bifocal glasses
Vergence
The amount of spreading of a bundle of light rays (wavefront) emerging from a point source
Direction of light travel must be specified (by convention, left to right)
Basic lens formula
Objects and images
Lenses
Vertex distance conversion
Pure cylindrical lens
power only in 1 meridian (perpendicular to axis of lens); produces focal line parallel to axis
Spherocylindrical lens
power in 1 meridian greater than other
Power cross diagram
depicts 2 principal meridians of lens with the power acting in each meridian (90° from axis), rather than according to axis (Figure 1-9)
Aberrations
Lenses behave ideally only near optical axis; peripheral to this paraxial region, aberrations occur
Spherical
shape-dependent aberration; periphery of lens has increasing prismatic effect; thus, peripheral rays refracted farther than paraxial ones, producing a blur interval along the optical axis (Figure 1-10)
Magnification
Angular
Example: moon gazing with telescope
MA = xD = D/4 (standardized to 25 cm [ m], the near point of the average eye)