GUIDED NOTES
Unit 14: Waves and Optics – Physical Optics
OBJECTIVES:1
IV. Waves and Optics
B. Physical optics
1. Interference and diffraction: Students should understand the interference and diffraction of
waves so they can:
a. Apply the principles of interference to coherent sources in order to:
1.) Describe the conditions under which the waves reaching an observation point from
two or more sources will all interfere constructively, or under which the waves from two
sources will interfere destructively.
2.) Determine locations of interference maxima or minima for two sources or determine
the frequencies or wavelengths that can lead to constructive or destructive interference
at a certain point.
3.) Relate the amplitude produced by two or more sources that interfere constructively
to the amplitude and intensity produced by a single source.
b. Apply the principles of interference and diffraction to waves that pass through a single or
double slit or through a diffraction grating so they can:
1.) Sketch or identify the intensity pattern that results when monochromatic waves pass
through a single slit and fall on a distant screen, and describe how this pattern will
change if the slit width or the wavelength of the waves is changed.
2.) Calculate for a single-slit pattern the angles or the positions on a distant screen
where the intensity is zero.
3.) Sketch or identify the intensity pattern that results when monochromatic waves pass
through a double slit, and identify which features of the pattern result from single-slit
diffraction and which from two-slit interference.
4.) Calculate for a two-slit interference pattern the angles or the positions on a distant
screen at which intensity maxima or minima occur.
5.) Describe or identify the interference pattern formed by a diffraction grating,
calculate the location of the intensity maxima, and explain qualitatively why a multipleslit grating is better than a two-slit grating for making accurate determinations of
wavelength.
c. Apply the principles of interference to light reflected by thin films so they can:
1.) State under what conditions a phase reversal occurs when light is reflected from the
interface between two media of different indices of refraction.
2.) Determine whether rays of monochromatic light reflected perpendicularly from two
such interfaces will interfere constructively or destructively and thereby account for
1
These are the outlined objectives of the AP Physics B course as laid out by the College Board. We will continue to
build this outline throughout the year. We do not do all of the objectives listed in the AP outline, as some are only
for AP Physics C. Therefore missing numbers or letters is intentional.
GUIDED NOTES
Newton’s rings and similar phenomena, and explain how glass may be coated to
minimize reflection of visible light.
2. Dispersion of light and the electromagnetic spectrum: Students should understand dispersion
and the electromagnetic spectrum so they can:
a. Relate a variation of index of refraction with frequency to a variation in refraction.
b. Know the names associated with electromagnetic radiation and be able to arrange in
order of increasing wavelength the following: visible light of various colors, ultraviolet light,
infrared light, radio waves, x-rays, and gamma rays.
NOTES
I. The _______________________________________
A. Electromagnetic waves: _________________________________ of electrical and magnetic
________________ that are carried through space by ______________________________________
called ________________
B. The _____________________ of the waves determines the characteristics of the radiation. The
spectrum of frequencies creates what is called the electromagnetic spectrum, which consists of the
following types, in order from short wavelength/high frequency to long wavelength/low frequency:




o
o
o


GUIDED NOTES
II. _______________________________
A. Interference basics:
1. ____________________________________ occurs at point P when waves from different
sources arrive _______________. ____________________________ together.
2. ____________________________________ occurs at point P when waves arrive from
different sources _____________________________.
3. Sketch:
GUIDED NOTES
4. _____________________________: When multiple sources2 create _____________________
________________________________________________at point P, they must be coherent
sources, meaning they ___________________________________________________________
(“_____________________”) so that the waves do not shift relative to each other over time.
B. Waves will interfere constructively at point P if the distance traveled by one wave is the same as,
or differs by an _____________________________________ from, the path length traveled by the
second wave. For the waves to interfere destructively, the path lengths must differ by an
______________________________________________________________
1. Condition for constructive interference: Path length difference
here
is an integer.
(Sketch)
2. Condition for destructive interference: Path length difference
(Sketch)
III. _________________________________________________
A. When light travels through small openings, such as a ______________, it ___________________.
This is called diffraction.
B. Diffraction occurs because the _____________________________________________________
___________________________________, or tiny spherical wave fronts. The ________________
____________________ created by the overlap of multiple wavelets is tangent to the wavelets.
(This is Huygens’ principle (1670.) It was the first to suggest that light behaves as waves. However,
his work wasn’t discovered until after Young’s experiment in 1803. (Below))
2
Sources (plural) means the source of each photon of light. These can be from the same emitter, as in a laser, or
from separate emitters, as we will see.
GUIDED NOTES
C. ___________________________________
1. A diffraction pattern consists of __________________________________________________
that occur where ________________________________________________________________
with each other when a single source of coherent light passes through a single slit or around a
small object onto a screen a large distance away (so that the __________ heading toward any
part of the screen can be considered ___________________.)
2. How diffraction patterns work:
a. Rays in the __________________ of the slit move ___________________________.
These make the _____________________ spot on the diffraction pattern (first image,
below.)
b. There is an angle where the rays are bent so that the __________ through the
__________________ of the slit are _____________________________________________
with waves from the ______________. At this angle, the waves _______________________
_________________________________ and make a ________________________ on the
screen. This angle is defined by _______________________where ____ is
_________________________.
c. There is an angle where the rays are bent so that the __________ through the
__________________ of the slit are _____________________________________________
with waves from the ______________, creating ___________________________. However,
the ______________________________ will ______________________________________
with waves from the __________________________. This creates a ___________________
GUIDED NOTES
that’s somewhat ______________________________________________. . This angle is
defined by _______________________.
Top half destroys
bottom half.
Bottom third destroys
middle third but
CONSTRUCTIVELY
interferes with top
third…dimmer than
central maximum but
still bright.
One quarter destroys
another quarter.
d. The pattern continues as the slit width is divided by integer parts (1/4, 1/5, etc.) to create
bands of brightness and darkness that obey the following where
is the slit width and
is
an integer.
1.) Minima:
2.) Maxima:
3.) _______________________________ (___________________): Maximum intensity
occurs at the center where
= 0⁰
GUIDED NOTES
e. Example 1: Light of wavelength 750 nm (red) passes through a slit 1.0E-3m wide.
Calculate the where the first minima will occur both in terms of a.) degrees and in terms of
b.) positions on a screen 20cm away? c.) How wide, therefore, is the central maxima?
d.) How could you increase the width of the maxima?
f. Example 2: When a monochromatic light source shines through a 0.2 mm wide slit onto a
screen 3.5 m away, the first dark band in the pattern appears 9.1 mm from the center of the
bright band. What is the wavelength of the light?
GUIDED NOTES
IV. ______________________________________________________
A. What the bro3 did:
1. Young passed monochromatic (single wavelength) light through two thin slits and projected
this light onto a screen.
2. If light were made of particles, the screen should have shown two beams of light from the
slits. However _________________________________________________________________,
_________________ that ________________________________________________________.
(Again, Huygens’ work wasn’t known even though it preceded Young’s work.)
B. The interference pattern of light passing through two slits resembles the pattern of diffraction
fringes.
1. The __________________ (________________________) is ___________________________
opposite the slits on the screen. It’s the ___________________ because both rays travel the
_____________________________.
2. ____________ occur where the _______________________________ is an _______________
number of wavelengths:
where
is the distance between the slits and
is the angle from the center of the slits to the fringe on the screen.
3. ____________ occur where the _______________________________ is an ______________
of ________________________________________.
3
Thomas Young completed his double-slit experiment in 1801.
GUIDED NOTES
GUIDED NOTES
4. Example 3: A screen containing two slits 0.100 mm apart is 1.20m from the viewing screen.
Light of wavelength 500 nm falls on the slits from a distant source. Approximately how far apart
will the bright interference fringes be on the screen?
5. Example 4: In a double-slit experiment with slit separation of 0.08 mm, blue light (440 nm)
gives a second-order bright fringe at a certain location on a flat screen. What wavelength of
visible light would produce a dark fringe at the same location? Assume that the range of visible
wavelengths extends from 380 nm to 750 nm.
6. Example 5: Look at Check your Understanding 2 on page 860 of your textbook. Solve and
explain.
GUIDED NOTES
V. _______________________________________
A. A diffraction grating is a _______________ with ________________________________________
______________________________________________.
B. Maxima & minima
1. The ____________________ occur where the _______________________ traveled equals
_______________________________ of the wavelength so that light from slit 1 is one
wavelength different from light from slit 2 and two wavelengths different from light from slit 3,
and so on.
2. _________________________ occur where the distance traveled equals _________________
multiples.
3. The ________________________ apply as with _________________________. The principal
maxima (central maxima) occur where
and lies on the central axis.
C. _________________________________
1. Resolution is the ____________________________ to _______________________________
__________________________________________.
a. When the two central maxima from the two sources overlap, they can’t be distinguished.
This is low resolution.
b. When the central maxima from one source overlaps the minima from the other, creating
a break in the light. This creates higher resolution.
2. A multiple-slit grating is better than a two-slit grating for making accurate determinations of
wavelength because the large number of slits increases the chance that destructive interference
will occur near the maxima, making them very narrow and, hence, sharper and easier to read
with precision. (See Giancoli, 5th ed., page 736 for a more complete explanation.)
GUIDED NOTES
D. Example 6: Calculate the first- and second-order angles for light of wavelength (a.) 400nm
(violet) and (b.) 700nm (red) if the grating contains 10,000 lines/cm.
SUMMARY OF DIFFRACTION AND INTERFERENCE
Single Slit Diffraction
Double Slit Interference
Diffraction Grating
Central maximum:
Central maximum:
Central maximum:
Secondary maxima:
Secondary maxima:
Secondary (and beyond)
maxima:
is for MINIMA, and d is the
is for MAXIMA, and d is the
is for MAXIMA, and d is the
width of the slit
separation of the slits
separation of the slits
GUIDED NOTES
VI. _____________________________: the _______________ of light when it passes from a medium of
one _____________ to a medium of another density
A. In a ________________, light travels at speed _____ = ___________________, but in
______________mediums, it _______________ down.
B. __________________________________________ , _______: A value unique to each medium
that refers to the extent to which light _______________ in that medium
_________________________________. The ____________________________, the ____________
the speed of light in that medium.
1. The index of refraction of light _________________________________________________.
2. ______________________________: When white light enters a medium at an angle, this
variation in
causes _________________________ to ________________________________.
This allows light to ______________, or disperse, into its component __________________.
VII. _____________________________________________________
A. When light enters a thin4 film (such as a layer of soap or oil floating on water,) some light reflects
from the top of the layer, and some penetrates the layer, refracts as it enters, reflects off the
bottom, and refracts as it exits again into the original medium.
4
For this to work, the thinness should be close to the wavelengths of the light involved.
GUIDED NOTES
B. ______________________________: When light _________________ off a surface of
__________________ index of refraction, the wave is ___________________ so that crests become
troughs, and troughs become crests. This _______________ the wave by _____________________.
Because the index of refractions of both media determines whether a phase shift occurs, each
situation is unique in terms of interference.
1. When
…
a. A phase shift occurs twice, so…
b. If the distance the light travels within the film (2x thickness, or
) equals an integer
multiple of the wavelength of the light5, constructive interference occurs; a half-integer
multiple results in destructive interference.
** Hence where ________________________, ______________________________ occurs.6
2. When
or the reverse…
a. A phase shift occurs once, so…
b. If the distance the light travels within the film ( ) equals a half integer multiple of the
wavelength of the light, constructive interference occurs; a whole integer multiple results in
destructive interference.
** Hence where ________________________, ______________________________ occurs.
5
When light travels through a medium, its frequency does not change. Therefore to account for the difference in
speed the wavelength changes.
6
Not on formula sheet. Know this conceptually.
GUIDED NOTES
C. Applications of thin-film interference:
1. Newton’s Rings7:

When a curved glass is placed in contact with a flat glass, a thin film of varying thickness
exists between the two pieces of glass such that it gets thicker farther from the center.

Therefore a varying pattern of constructive and destructive interference emerges,
producing rings.
2. Non-reflective coatings

A very thin film of a material whose index of refraction is the average of air and glass is
put on the glass surface. This means that a phase shift will occur twice. Next, the
thickness is adjusted so that

so that destructive interference occurs.
This destructive interference is optimized for the center of the visible light spectrum.
Therefore red and blue still gets reflected, making a lens with non-reflective coating
appear purple.
7
Newton believed light was a particle. He actually proved that it was a wave by noting this ring phenomenon,
although he never realized it. True to Newton, of course, is that someone else, his rival Robert Hooke, discovered it
first, but Newton received the credit because he studied it in more depth.