Studying for the Exam

• Relevant chapters: E, 1, 2 & 3• To prepare for the exam it is helpful to …

– review readings– review lecture notes online (esp. concept

questions)– revisit homework– look over the activities

Studying for the Exam

• Filter out the relevant information, don’t focus on details

• Properties of relevant information:– Information appears repeatedly in course

materials (readings, slides, homework,…)– It is not an isolated fact, but can be “reasoned

out”– It is an important concept (e.g. daily &

monthly motion, scientific method)

Exam Questions

• About 30 multiple choice questions• A few short answer problems• Types of questions NOT on the exam:

– What’s Galileo’s birth year?– What is the frequency of yellow light?– What is the distance of the Earth to the Sun?– What is the mathematical formula for the

Hydrogen energy levels?

Exam Questions

• Types of questions that could be on the exam: – Why isn’t there a lunar eclipse every full moon?– It is noon in Westerville. Is it earlier/ later/different

day/different season in Paris, France? – What is the difference between a sidereal and a solar

day? – How high above the horizon is the polar star at noon if

you are at 23 degrees northern latitude? – Given the wavelength of yellow light, what is its

frequency?

Doppler Shift

• From Wikipedia

Doppler Shift

• Can use the Doppler shift to determine radial velocity of distant objects relative to us

• Transverse velocity can be measured from the motion of stars with respect to back-ground over a period of years

Homework: Doppler Shift of Hydrogen spectrum

• The discrepancy between the wavelength of a line measured in the lab versus measured on an object is proportional to the velocity of the object

• Apparent/ true wavelength = 1+ velocity/c • Example:

– Observed(or apparent): 698 nm– Actual(or true or lab) wavelength: 656.3nm– velocity = (698nm/656.3nm -1) c = 19100 km/s

Atomic Energy Levels

• For Hydrogen, the energies of the atomic levels are given by a simple formula that just depends on the (excitation) number n of the orbit: En = – Ry / n2

where Ry = 13.6 eV = 2.179 x 10-18J E1, E2=¼ E1, E3=1/9 E1,…

• Electrons in higher levels will cascade down, producing many different spectral lines

• Formula can be converted to frequency, wavelength

Light hits Matter: Refraction• Light travels at different speeds in vacuum, air,

and other substances• When light hits the material at an angle, part of it

slows down while the rest continues at the original speed – results in a change of direction– Different colors bend different amounts – prism,

rainbow

Application for Refraction

• Lenses use refraction to focus light to a single spot

Light hits Matter (II): Reflection• Light that hits a mirror is

reflected at the same angle it was incident from

• Proper design of a mirror (the shape of a parabola) can focus all rays incident on the mirror to a single place

Application for Reflection

• Curved mirrors use reflection to focus light to a single spot

Telescopes

• From Galileo to Hubble

Telescopes• Light collectors• Two types:

– Reflectors (Mirrors)– Refractors

(Lenses)• Magnification:

– ratio of focal lengths of objective and eyepiece

– M = fobj/feye– Example:

2000mm telescope with 40mm eyepiece: 50x

Reflecting Telescopes

Problems with Refractors

• Different colors (wavelengths) bent by different amounts – chromatic aberration

• Other forms of aberration• Deform under their own weight• Absorption of light• Have two surfaces that must be optically

perfect

Telescope Size• A larger telescope gathers more light (more

collecting area) • Angular resolution is limited by diffraction

of light waves; this also improves with larger telescope size

Resolving Power of Telescopes

Andromeda Galaxy Telescope 1 Telescope 2 of double size

Resolving Power of Telescopes (II) Andromeda

Galaxy

Resolution:(a) 10’(b) 1’(c) 5”(d) 1”

Magnification

• The magnification of a telescope can easily be changed by plugging in a different eyepiece with a different focal length

• M= focal length of main lens or mirror focal length of eyepieceExample: F= 2000mm, f = 40 mm M= 50

Atmospheric Limitations

Atmospheric Limitations

Radio Window

Optical Window

IR Window

Largest Earth-Based Telescopes• Hobby-Eberly Telescope,

Davis Mountains, TX– 11 m diameter– Cannot see all parts of the sky

• Keck I and II, Mauna Kea, HI– 36 1.8 m hexagonal mirrors;

equivalent to 10 m– Above most of atmosphere

(almost 14,000 ft ASL)– Operating since 1993

Other Techniques

• Put telescopes on satellites– Hubble Space

Telescope: 2.4 m, since 1990

• Use computers to correct optics during light gathering: adaptive and active optics

• Interferometry• Radio astronomy

Other Wavelengths• Must be carried out on satellites (or rockets,

balloons, etc.) due to strong absorption in the atmosphere

• Infrared astronomy• High-energy (UV, X-ray, gamma-ray) astronomy

Full-Spectrum Coverage

Each region of the electromagnetic spectrum gives us valuable information about the universe

(only these frequency bands can be observed with ground-based telescopes)

• Radio

• Infrared

• Visible

• X-Ray

• Gamma-ray