Optics
- see also:
- see web articles:
Reflection:
- laws of reflection:
- the angle of incidence = the angle of reflection
- the incident ray, the reflected ray & the normal to the surface
lie in the same plane
- spherical mirrors:
- principal focus is the convergence point for rays parallel to &
close to the principal axis of the mirror, and is located halfway
between the mirror & its centre of curvature, ie. focal length =
radius/2
- the mirror equation:
- if p = distance of object from mirror of focal length f, then q =
distance of image from mirror
- 1/p + 1/q = 1/f
- magnification = q/p;
Refraction:
- speed of light depends on the medium in which it travels (water = 3/4 that
in air)
- refraction (change of direction) occurs when light passes from a medium of
one density to a medium of another density
- a material of lesser speed is called "optically more dense"
- refractivity of a medium:
- absolute index of refraction:
- absolute index of refraction of a medium = speed in vacuum /
speed in medium (this is dependent on wavelength!)
- examples for wavelengths of 5893A:
- air = 1.0003; crown glass = 1.517; diamond = 2.419; quartz =
1.4585; ice at -8degC = 1.31; water at 20degC = 1.333;
- relative index of refraction:
- relative index of refraction of 2nd medium relative to first =
speed in medium 1 / speed in medium 2 = abs. index medium 2 / abs. index
medium 1
- optical dispersion:
- the variation of the index of refraction with the wavelength of
light is called the optical dispersion of a substance
- short wavelengths are refracted more than long wavelengths
- substances with high optical dispersion, usually also have a high
index of refraction (eg. diamond)
- Snell's law:
- for a given wavelength & a pair of substances, the ratio of the
sine of the angle of incidence (i) to the sine of the angle of
refraction (r) is constant
- abs.index medium 1 * sin i = abs.index medium 2 * sin r
- examples:
- underwater viewing:
- the apparent depth of an object under water when viewed from above
the water, is less than its actual depth below the surface
- real depth = 1.333 x apparent depth (1.333 is the rel.index of
water to air)
- mirages:
- on still sunny days, there may be a layer of hot, expanded air in
contact with the heated ground in which light travels faster, thus
light entering it obliquely will be refracted upwards resulting in
observer seeing inverted images of distant objects suggestive of
reflections in a smooth pool of water. These are often seen on
highways.
- looming:
- when the air near the ground is cooler than the upper strata (eg.
over snow or over water), rays of light are deviated downward, thus
one may see an image of a ship above the ship itself, or the
curvature may allow one to see objects below the horizon.
-
- total internal reflection:
- for light passing from a medium to a less dense medium, there is an
incident angle whereby refraction will no longer occur & the light
is internally reflected instead, this occurs as the angle of refraction
approaches 90deg. (when sin r = 1)
- thus critical angle of incidence (ic) can be
determined from sin ic = abs.index medium 2 / abs.index
medium 1
- therefore, for water/air interface when viewed from under water, the
critical angle is 48deg.
- spherical surfaces:
- for rays with small angles to perpendicular of surface:
- if p = distance of object from mirror of focal length f, then q =
distance of image from mirror
- abs.index medium 1/p + abs.index medium 2/q = (abs.index medium
2 - abs.index medium 1)/radius
- by convention, radius is positive if measured from surface to
centre in direction of light leaving the surface.
- thin lenses:
- if the object is at infinity, the image is at the principal focus
- thin lens equation:
- if p = distance of object from lens of focal length f, then q =
distance of image from lens
- 1/p + 1/q = 1/f and magnification = q/p
- power of a lens:
- the amount by which it can change the curvature of a wave (in diopters)
= 1/focal length in metres, thus a +2 is a convex lens with focal
length of 500mm
- when using multiple lenses, just sum the diopter values to get the
total diopter value
- positive diopter lenses are similar in shape to the convex lenses
found in common magnifying glasses.
- negative diopter lenses may use concave elements, but this shape
may be masked by multiple glass elements.
- photographers will most often encounter diopter lenses as a kit of
+1, +2, +3, and +4 diopter lenses for macro-photography.
- for a camera lens focussed at infinity, adding a closeup
positive diopter lens will change the focus to (1/diopter value)
in meters. So a +4 diopter lens will be 1/4 meter, a +10 diopter
lens will be 1/10th meter (4 inches), and a +20 diopter lens
will be only 1/20th of a meter or about 5 cm. (or 2 inches).
- the new effective focal length in metres = camera lens focal
length in meters / (1+ diopter value*focal length in
metres)
- the effective f/ratio will be altered as the aperture stays
the same but you now have a new focal length
- combinations of lens:
- when lenses are used in combination, each magnifies the image from
the preceding lens, thus resultant magnification is the product of
individual magnifications.
- when thin lenses are in contact, total power is sum of the powers,
ie. 1/f = 1/f1 + 1/f2
- aberrations:
- spherical aberration:
- rays that enter the lens near its edge are brought to focus
closer to the lens than are the central rays resulting in
spherical aberration
- this can be minimised by using a diaphragm in front of the
lens to decrease its effective aperture, although the sharper
image will be at cost of less light.
- coma:
- another form of spherical aberration occurs for object points
that are laterally displaced from the principal axis
- this can be minimised by using a compound lens having several
surfaces, or more simply by an aperture stop that eliminates
rays which are not near the principal axis
- astigmatism:
- a lens defect whereby horizontal & vertical lines in an
object are brought to a focus in different planes
- arises from a lack of symmetry of a lens or lens system about
the line from the centre of the lens to an object.
- see also: photographic
astigmatism and field curvature
- distortion:
- caused by fact that magnification varies at different parts of
the image and may produce barrel-shaped or pin-cushion
distortion.
- chromatic aberration:
- as a result of optical
dispersion, short wavelengths are refracted more than long
wavelengths, resulting in fringes of colour around an object
- its presence resulted in Newton inventing the reflecting
telescope which does not have this aberration
- it can be corrected in lens by combining a strong positive
lens made of glass with a low dispersion, with a weak negative
lens of highly dispersive glass. Each component has a difference
of power for two colours & if these are equal in magnitude
but of opposite sign, then they will cancel with a net power of
zero. Such a lens is called an achromatic lens.
- new types of glasses such as flourite and ED invented in the
1990's are even better at minimising chromatic aberration and
these are called apochromatic (APO).
- field curvature
- anastigmatic lens:
- a lens corrected for such defects as spherical aberration,
astigmatism, distortion & chromatic aberration.