Ch 17 physics
A wave that reflects from a surface at which the index of refraction increases
has a phase change.
When a light wave enters a material, the only way it can go slower while oscillating at the same frequency is to
have a shorter wavelength.
Liquids and solids have higher indices of refraction than gases, simply because they have a much
higher density of atoms for the light to interact with
two reflected waves will interfere constructively to cause a strong reflection if they are
in phase (i.e., if their crests overlap)
the wave model
Under many circumstances, light exhibits the same behavior as sound or water waves.
The pair of slits is called double slits, and in a typical experiment they are
approximately .1 mm wide and spaced approximately .5 mm apart
If a wave moves from a string with a higher wave speed to a string with a lower wave speed, the reflected wave is inverted with respect to the
incoming wave.
the number of lines per millimeter is simply the
inverse of the slit spacing d in millimeters.
If neither or both waves have a phase change due to reflection, the net addition to the path-length difference
is zero
larger values of the wavelength imply
larger diffraction angles (theta m)
dark bands happen from destructive interference from crests and troughs which happens with
light as welll as with sound
The ray model: The properties of prisms, mirrors, lenses, and optical instruments such as telescopes and microscopes are best understood in terms of
light rays, straight-line paths that light follows
Being self-sustaining means that electromagnetic waves require no
material medium in order to travel
diffraction grating
multi-slit device
The spreading of diffraction becomes noticeable only when an opening or object is "
narrow," comparable in size to the wavelength of the wave.
The bright fringes of a diffraction grating are much
narrower.
If the two reflected waves are out of phase, with the crests of one wave overlapping the troughs of the other, they will interfere destructively to cause a weak reflection or, if their amplitudes are equal,
no reflection at all.
Photons are the quanta
of light
The ray model of light is the basis
of ray optics
Interference occurs between the waves reflected from the two surfaces of a thin film with index
of refraction n
If only one wave has a phase change due to reflection, the effective path-length difference is increased by
one half-wavelength
the frequency of a wave does not change as the wave moves from
one medium to another.
two slits has broad central spots from
overlapping
Diffraction is the spreading of a wave after it
passes through an opening
Bright fringes are seen on the viewing screen at positions where the
path-length difference delta r between successive slits is equal to (m)(wavelength) where m is an integer
The wavelets going straight forward all travel the same distance to the screen. Thus they arrive in
phase and interfere constructively to produce the central maximum
a light wave undergoes a phase change if it reflects from a boundary at which the index of
refraction increases.
N light waves, from N different slits, will all be in phase with each other when they arrive at a point on the screen at angle
theta m
The interference of light waves reflected from the two boundaries of a thin film, such as the thin film of water that makes a soap bubble, is called
thin-film interference
phase change, is equivalent to adding an extra half-wavelength
to the distance the wave travels
The superposition of these wavelets produces the
diffraction pattern on the screen
The wavelength inside the material decreases, but the frequency
doesn't change
white light" is
all the colors, or wavelengths, combined.
A thin film can reduce reflection, but it can
also enhance reflection
wavelengths of light are extremely small, ranging from about
400 nm for violet light to 700 nm for red light
diffraction
After passing through the opening, the wave spreads out to fill the space behind the opening
The diameter of the diffraction pattern increases with distance L, showing that light spreads out behind a circular aperture, but it decreases if the size .
D of the aperture is increased
In Figure 17.6b, suppose that for some point P on the screen r1 = 5,002,248.5λ and r2 = 5,002,251.5λ, where λ is the wavelength of the light. The interference at point P is
Interference depends on the path-length difference. Here a difference of 3λ—a whole number of wavelengths—signifies constructive interference.
If we increase d, the spacing between the two slits, how will this change the spacing of the bright fringes on the screen?
The fringes will get closer together.
White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow,
The red side is farthest from the center of the screen, the violet side is closest to the center.
Reflections from a thin layer of air between two glass plates cause constructive interference for a particular wavelength of light λ. By how much must the thickness of this layer be increased for the interference to be destructive?
To go from constructive to destructive interference, the path-length difference must increase by λ/2. Light passes through the air layer twice, so the thickness needs to be increased by only half this, or λ/4.
reflection grating
a mirror with hundreds or thousands of narrow, parallel grooves cut into the surface.
Equal-frequency light waves are produced when partial reflection at a boundary splits a light wave into
a reflected wave and a transmitted wave
Each point on the wave front is paired with another point at distance
a/2 away
Only when the size of an object or an opening approaches the wavelength of light does
diffraction become important.
To observe interference, we need two light sources whose waves
can overlap and interfere
a single slit of width a has a bright
central maximum of width that is flanked by weaker secondary maxima
Structural Color
color that depends not on pigment, but on an object's structure.
a reflection grating can be made by
cutting parallel grooves into a mirror surface
There's no phase change at a boundary where the index of refraction
decreases.
These wavelets all meet on the scree at angle theta. Wavelet 2 travels distance
delta r= (a/2) sin theta farther than wavelet 1
a light wave is partially reflected from any boundary between two transparent media with
different indices of refraction.
light waves are a "self-sustaining oscillation of the
electromagnetic field
And the wavelength of light is
extremely short.
The index of refraction of a material is always
greater than 1
The wavelength in the transparent material is
shorter than the wavelength in a vacuum
Larger values of m lead to
shorter wavelengths
Waves overlap as they spread out behind
slits.
each point on the wave front can be thought of as the
source of a spherical wavelet.
When light waves pass through a narrow slit, they too
spread out behind the slit
something quite different occurs when we make the opening much wider. Rather than spreading out, now the wave continues to move
straight forward, with a well-defined boundary between where the wave is moving and its "shadow," where there is no wave.
It is not inverted if the wave moves from a string with a lower wave speed to a
string with a higher wave speed.
The wave front at a later time is
tangent to all the wavelets
as the number of slits N increases,
the bright fringes get narrower and brighter
The mother of pearl, or nacre, layer inside an abalone shell is made largely of transparent materials, but the interaction of light with complex structures produces
the bright, striking colors
the bright fringes are labeled by the integer m, starting at
the central maximum
The slowdown is a consequence of interactions between the electromagnetic field of the wave and
the electrons in the material
shortest wavelength corresponds to
the largest index of refraction.
the short wavelengths scatter much more than
the long wavelengths
The smaller the opening a wave squeezes through,
the more it spreads out on the other side
central maximum is significantly brighter than
the secondary maxima.
central maximum is significantly broader than
the secondary maxima.
index of refraction of a material determines
the speed of light in that material
The spread of colors seen with a prism, or in a rainbow, is called
the visible spectrum
For an aperture of any shape, a smaller opening causes a greater spreading of
the wave behind the opening.
the wave model: The bright colors of a hummingbird and the blue of the sky are best understood in terms of
the wave model of light
The constructive interference between these wavelets produces the central maximum of the diffraction pattern at
theta = 0
Constructive and destructive interference are due to the overlap of
two or more waves as they spread behind openings
Thus light is partially reflected not only from the front surface of a sheet of glass, but from the back surface as well, as it exits from the glass into the air. This leads to the
two reflections
If the wavelengths of light are incredibly small, the oscillation frequencies are
unbelievably high
The wavelength in a material with index of refraction n is shorter than the wavelength
vac in a vacuum
Light waves travel with speed c in a vacuum, but they slow down as they pass through transparent materials such as
water or glass or even, to a very slight extent, air
The study of light as a wave is called
wave optics
The Photon Model: In the quantum world, light consists of photons that have both
wave-like and particle-like properties.
constructive interference occurs when r1 and r2 differ by a
whole number of wavelengths
Deconstructive interference occurs when r1 and r2 differ by a
whole number or wavelengths plus half a wavelength
narrower slit (smaller a) causes a
wider diffraction pattern.