Light
Visible light has very small wavelengths in the range 700
nanometers (red) to 400 nanometers (violet). Newton was the
first to understand colors by doing experiments with prisms
that separate white light into a spectrum of colors. Red, green,
blue are pure colors, but white light is a mixture of colors.
Black is no light at all.
• Light sources
Light is emitted by individual atoms acting as tiny antennae.
All bodies emit electromagnetic waves depending on their temperature. Incandescent solids, such as the glowing filament in
a light bulb, emit a continuous (no gaps) spectrum of electromagnetic waves whose wavelengths and intensity depend on
the temperature of the body but do not depend very much on
the material. If the temperature is not very high (such as our
human bodies) the radiation is typically infrared. When the
body is hot enough it glows red, hotter it glows white, even
hotter it glows bluish. This is called thermal radiation. It is
also called black body radiation because a black surface is the
best absorber and also the best emitter.
In contrast, incandescent (hot) gases emit a discrete, or line,
spectrum, in which certain colors are present, with gaps between them. The colors present are characteristic of the gas,
and can be used to identify the gas. The figure above shows
the line spectra of Li (lithium), Na (sodium), etc. The colors
can be separated with a prism, but it is better to use a diffraction grating. The simplest and most important spectrum is
the hydrogen spectrum, which was explained theoretically by
Niels Bohr, in what was the first triumph of what would lead
to Quantum Mechanics.
The figure above shows the emission and absorption spectra of
hydrogen. When white light, which has all the colors, passes
through a cloud of cold hydrogen, it absorbs the colors that it
emits when it is hot.
Geometrical Optics or Ray Optics
We are accustomed to think that light travels along rays in
straight lines. Actually the light is a wave, and the rays are
perpendicular to the wave fronts. The idea that light travels in
straight lines comes from observing sharp object outlines and
sharp shadows.
illuminated wall
light rays
light source
sharp shadow
opaque object
wall or screen
This approach is valid whenever diffraction is negligible, which
is the case when the wavelength of light is much smaller than
objects or apertures in its path. Visible light has very small
wavelengths in the range 700 nanometers (red) to 400 nanometers (violet), so ray optics applies in most cases.
There are three laws of Ray optics:
(1) In a medium where the speed of light is uniform light rays
travel in straight lines. When the medium is not uniform, such
as over the hot surface of a road, the rays can bend. This is
the cause of the appearance of water on a distant road surface.
Actually, rays from the sky bend upward as they pass near the
road, and we see those rays coming from the road.
When light passes from one transparent material into another
there is a reflected ray and a transmitted ray. The normal is a
line perpendicular to the surface of separation of the two media.
(2) The law of reflection: The reflected ray makes the same
angle θ1 with the body surface as the incident ray.
the normal
incident ray
θ1
θ1
reflected ray
first medium, index n1
second medium, index n2
refracted ray
θ
2
The transmitted ray is refracted (bent) depending on the indices of refraction of the two materials. The speed of light is different through vacuum, glass, water, etc. In vacuum the speed
is c. The speed of light through a material is v = c/n, where n
is the index of refraction of the material. Thus, nvac = 1,
nair = 1.00029, nwater = 1.33, ncrown glass = 1.52,
ndiamond = 2.42, etc.
(3) The law of refraction: The angle θ2 that the refracted ray
makes with the normal obeys n1 sin θ1 = n2 sin θ2 , where sin θ
is the tigonometric sine of the the angle. Therefore, if n2 > n1 ,
then θ2 < θ1 , so as light goes from air into glass it is bent
toward the normal.
The three laws can be explained in term of Fermat’s principle
of least time: In going from one point to another a light ray
follows a path of least time”.
• Images:
A film of film is exposed to a person in front of it. No image
is produced on the film because light from any point on the
person goes to every point on the film. There is no one-to-one
correspondence between point on the person and points on the
film. The film will simply appear gray all over.
light rays from the nose fall all over the film
film
light rays from the head fall all
over the film
There is no one-to-one correspondence between points on
the person and points on the film
No image is produced
A converging lens focuses parallel rays (as if coming from a
very distant object) at a distance from the length called the
focal distance. A real image of an object can be formed if the
distance from the object to the lens is greater than the focal
distance of the lens f in the figure below.
converging lens
object
real image
f
f
focal distance f
eye
The focal length is the reciprocal of the power, so a lens of 2
diopters has a focal length of 0.5 meter. In the figure above
the image is called real because light actually goes there. In a
photographic camera the film should be placed where the real
image is to get a sharp image. If the film is in front, or behind,
that point, the rays keep going and make a fuzzy image on the
film. If no film is placed there the light keeps going and our eye
will see an inverted image “in the air”. The figure below shows
more or less what happens with a converging lens in a camera.
An ideal converging lens is able to take all the light rays from
the nose and focus at one point on the film. A real lens focuses
them into a small ”circle of confusion”. The lens does this not
just for the nose, but for every point on the person. A real
inverted image is made on the film.
light rays from the nose all go to one point on the film
film
light rays from the head also go to
one point on the film
There is a one-to-one correspondence between points on the
person and points on the film
A real inverted image is produced
Say a point source of light emits light is all directions. Only
a small diverging cone of rays enters the pupil of our eyes and
the lens power of the eye forms a real inverted image in the
retina. This diverging cone of rays is all our eye needs to ”see”
the point. When we stand in front of a mirror the rays go as
in the figure below.
eye
object
the normal
incident rays
1
2
1
2
reflected rays
mirror surface
diverging cone of rays
virtual image
There is nothing here but
light seems to come from
the virtual image.
We “see” the virtual image behind the mirror, where there is
a brick wall. There is really no light actually there, but the
diverging cone of rays seems to come from there.