Review for exam 4

As with all other powerpoint exam reviews for this course, this is not a complete review:

– It consists only of a collection of slides I was able to find and adapt for this purpose.

– There are topics covered in your homework (and which may therefore appear on an exam) that are not included in this review.

Chap 17Sections 1-4

Light and Image Formation

Reflection; Image Formation by a Plane Mirror

Law of reflection: the angle of reflection (that the ray makes with the normal to a surface) equals the angle of incidence.

Reflection; Image Formation by a Plane Mirror

What you see when you look into a plane (flat) mirror is an image, which appears to be behind the mirror.

Reflection; Image Formation by a Plane Mirror

This is called a virtual image, as the light does not go through it.

For a plane mirror, the distance of the image from the mirror is equal to the distance of the object from the mirror.

Formation of Images by Curved Mirrors

Curved mirrors may be reflective on either the inside (concave) or outside (convex).

Index of RefractionIn general, light slows somewhat when traveling through a medium. The index of refraction of the medium is the ratio of the speed of light in vacuum to the speed of light in the medium:

Refraction: Snell’s Law

Refraction is what makes objects half-submerged in water look odd.

Refraction: Snell’s Law

Light changes direction when crossing a boundary from one medium to another. This is called refraction, and the angle the outgoing ray makes with the normal is called the angle of refraction.

Law of refraction (Snell’s law):

For small angles:

1 1 2 2n n

Thin Lenses; Ray Tracing

Parallel rays are brought to a focus by a converging lens (one that is thicker in the center than it is at the edge).

Thin Lenses; Ray Tracing

A diverging lens (thicker at the edge than in the center) make parallel light diverge; the focal point is that point where the diverging rays would converge if projected back.

Thin Lenses; Ray Tracing

Thin Lenses; Ray Tracing

For a diverging lens, we can use the same three rays; the image is upright and virtual.

The Thin Lens Equation

The distances:

i from the lens to the image

o from the lens to the object

f the focal length of lens

Are related by the lens equation:

1 1 1

o i f

Chap 18The atom

Planck’s Quantum Hypothesis; Blackbody Radiation

Max Planck in 1900:

The energy of atomic oscillations within atoms cannot have an arbitrary value; it is related to the frequency:

The constant h is now called Planck’s constant.

Planck’s Quantum Hypothesis; Blackbody Radiation

Planck found the value of his constant:

Planck’s proposal was that the energy of an oscillation had to be an integral multiple of hf. This is called the quantization of energy.

Early Models of the Atom

It was known that atoms were electrically neutral, but that they could become charged, implying that there were positive and negative charges and that some of them could be removed.

One popular atomic model was the “plum-pudding” model:

Early Models of the Atom

The plum-pudding model had the atom consisting of a bulk positive charge, with negative electrons buried throughout.

Early Models of the Atom

Rutherford did an experiment that showed that the positively charged nucleus must be extremely small compared to the rest of the atom.

He scattered alpha particles – helium nuclei – from a metal foil and observed the scattering angle.

He found that some of the angles were far larger than the plum-pudding model would allow.

Early Models of the AtomThe only way to account for the large angles was to assume that all the positive charge was contained within a tiny volume – now we know

that the radius of the nucleus is 1/10000 that of the atom.

Early Models of the Atom

Therefore, Rutherford’s model of the atom is mostly empty space:

The Bohr Atom

Bohr proposed that the possible energy states for atomic electrons were quantized – only certain values were possible. Then the spectrum could be explained as transitions from one level to another.

Chap 19The nucleus and nuclear energy

Nuclear Reactions

A nuclear reaction takes place when a nucleus is struck by another nucleus or particle.

An example:

Nuclear Fission

After absorbing a neutron, a uranium-235 nucleus will split into two roughly equal parts.

One way to visualize this is to view the nucleus as a kind of liquid drop.

Nuclear Fission

The energy release in a fission reaction is quite large. Also, since smaller nuclei are stable with fewer neutrons, several neutrons emerge from each fission as well.

These neutrons can be used to induce fission in other nuclei, causing a chain reaction.

Nuclear Fission; Nuclear Reactors

In order to make a nuclear reactor, the chain reaction needs to be self-sustaining – it will continue indefinitely – but controlled.

Neutrons that escape from the uranium do not contribute to fission. There is a critical mass below which a chain reaction will not occur because too many neutrons escape.

Nuclear Fission; Nuclear Reactors

Nuclear Fusion

The lightest nuclei can fuse to form heavier nuclei, releasing energy in the process.

An example is the sequence of fusion processes that change hydrogen into helium in the Sun. They are listed here :

Chap 20Sections 1-3

Special Relativity

Relativity

Definition of an inertial reference frame:

• One in which Newton’s first law is valid

• Earth is rotating and therefore not an inertial reference frame, but can treat it as one for many purposes

• A frame moving with a constant velocity with respect to an inertial reference frame is itself inertial

Relativity

Relativity principle:

The basic laws of physics are the same in all inertial reference frames.

Einstein’s Postulates of the Special Relativity

1. The laws of physics have the same form in all inertial reference frames.

2. Light propagates through empty space with speed c independent of the speed of source or observer. In other words, the speed of light is the same in all inertial reference frames.

Simultaneity

One of the implications of relativity theory is that time is not absolute. Distant observers do not necessarily agree on time intervals between events, or on whether they are simultaneous or not.

In relativity, an “event” is defined as occurring at a specific place and time.

Time DilationA different thought experiment, using a clock consisting of a light beam and mirrors, shows that moving observers must disagree on the passage of time.

Chap 21Sections 1-3

Quarks & Cosmology

Elementary Particle Physics

the four known forces

Particles and Antiparticles

The positron is the same as the electron, except for having opposite charge. We call the positron the antiparticle of the electron.

Quarks

Here are the quark compositions for some baryons and mesons:

Quarks

This table gives the properties of the six known quarks.