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.