Daniel Vlk
Department of Biophysics
Wave properties of light
Electromagnetic character of light. B – magnetic flux
density, E – intensity of electric field, l = wavelength.
Light can be described in terms of wave motion. The light waves are harmonic oscillations
of an electromagnetic field – the vectors of magnetic flux density and intensity of
electric field oscillate perpendicularly to the direction of light propagation.
Let us start from the speed (velocity) of light:
where T is the period of oscillations [s], f is their frequency [s-1], and l is their wavelength
[m]; n is the index of refraction, and c is the speed of light in vacuum. Remember that
the previously mentioned index of refraction depends strongly on the frequency or
wavelength of light. The index of refraction increases with decreasing wavelength.
Remember the relation mentioned in the paragraph about chromatic aberration:
nred < nyellow < nviolet.
Wave properties of light
n
c
f
T
v === λ
λ
Therefore, the most refracted light is the violet light. According to the last equation we
can write: then: hence:
where f is the frequency of the light, c is the speed of light in a vacuum, v is the speed
of light in given medium, λ is the wavelength of light in the given medium, and λ0
is the wavelength of light in vacuum.
Wave properties of light
λλ
vc
f ==
0 λ
λ0
== n
v
c
n
0λ
λ =
Huygens´ principle
All the point of a wavefront of light
thought of as new sources of smaller waves
These smaller waves expand in every direction and are in stepwith one another
Wave properties of light
Interference of light:
Interference of light and related phenomena can be observed with beams of coherent
light rays, i.e. rays of the same frequency and the same phase shift at a given
distance from the source of light. Interference is a result of superposition (addition,
summation) of oscillating vectors characterising the electromagnetic field.
Wave properties of light
Diffraction of light:
Light diffraction is a change of light propagation direction which occurs when light is
incident on particles, holes, slits etc. the dimensions of which are comparable with
the wavelength of light. It often demonstrates itself as the scattering of light. Light
rays diffracted at openings, slits, double slits or diffraction gratings can interfere
with each other. Therefore, we can observe also diffraction-conditioned interference
phenomena.
Wave properties of light
Diffraction grating
Reflection grating
Wave properties of light
Polarised light
As already explained, visible light consists of electromagnetic waves which are characterised by vectors
of E (electric field intensity) and B (magnetic flux density). These vectors oscillate perpendicularly
to the direction of light propagation. If the light beam consists of more rays, their B and E vectors
can either oscillate in many planes or only in a single plane (two perpendicular planes when
considering both B and E). Such a plane is called the polarisation plane. In the first case we speak
about non-polarised light, in the second case about polarised light.
Wave properties of light
Light waves can be polarised by several different means:
- by polarisation filters (polaroids, e.g. in sun glasses). Such a filter can be passed through only by
light the polarisation plane of which has an orientation allowing the passage.
- by reflection (the light reflected from glass, mirrors, polished surfaces etc. is partly polarised – this
causes reflected light is reduced in intensity by polarised sun glasses.
Wave properties of light
- Polarisation by double refraction (birefringence, encountered in anisotropic crystals, e.g. the Nicol
prism). In this phenomenon, the original ray is split into two parallel rays polarised perpendicularly.
Wave properties of light
Optically active substances (in a crystal form or in a solution) are able to rotate the plane of polarised
light. Many organic substances of great biological importance are optically active. It is possible, for
example, to measure the rotation angle of polarised light which depends on the concentration of the
substance through which the polarised light passed. The concentration of sugars is often measured
in this way. The measurement is done by means of instruments called polarimeters.
Wave properties of light
A relatively frequent task is to measure the quantity of light emitted by a body or incident on an illuminated surface.
Therefore we will briefly mention some of the most important photometric quantities used in the SI system.
Note: We always assume that the source of light radiates equally in all directions.
The luminous intensity I is the measure of light produced by a source of unit area in unit time. Its unit, candela [cd]
belongs among the fundamental SI-units. The candela can be defined by the following statement:
1 cd is one sixtieth of the luminous intensity of a “black body” source, 1 cm2 in cross-section area, at the temperature
of the platinum melting point (1755 °C), under normal atmospheric pressure and viewed at right-angles to the
area.
A new definition since 1979: The candela is the luminous intensity, in a given direction, of a source that emits
monochromatic radiation of frequency 540 × 1012 Hz and that has a radiant intensity in that direction
of 1∕683 watt per steradian
Note: A black body does not reflect light, it can only emit light.
An introduction to photometry
Luminous flux Φ is the measure of the amount of light emitted into a defined solid angle W. Its unit is called lumen
[lm]:
1 lm is the luminous flux produced by a point source of luminous intensity 1 cd into a solid angle of 1 sr (steradian).
Suppose that a 1-cd point source is at the centre of a hollow sphere with radius r = 1 m (called “unit sphere”). A
luminous flux of 1 lm will pass through an area of 1 m2 on the sphere surface.
[lm] [cd],
where ΔΩ is the solid angle in steradians [sr].
Simply – Luminous flux is the light outpu of a source measured in all directions (a lamp receives watts and emit
lumens). The measure of success of doing this is called efficacy and is measured in lumens per watt(lm/W).
An introduction to photometry
∆Ω
∆Φ
=⇔∆Ω=∆Φ II
The illumination (illuminance) E [lm.m-2 = lx – lux] expresses the amount of light incident onto a surface.
Definition: Luminous flux of 1 lm per 1 m2 produces an illumination of 1 lux.
An introduction to photometry