Lecture 8

Question 1

General scheme of adaptive optics

Answer 1

Laser guide star + natural guide star

Question 2

Spectral lines

Answer 2

stellar bodies emit radiation at a variety of wavelengths

emission if spectra is hot

absorption spectre if cold (lit)

Question 3

what can be determined by observing a stellar bodies spectrum

Answer 3

its chemical composition

Question 4

doppler shift

Answer 4

large planets cause star to ‘wobble’ leading to a doppler shift

Question 5

Resolving power

Answer 5

R = λ/Δλ = mN

Question 6

spectrometer

Answer 6

tune wavelength by rotating grating

Question 7

spectrograph

Answer 7

spectrum recorded on camera

Question 8

slit-less spectrographs

Answer 8

spectrographs made without a slit

Question 9

prisms

Answer 9

disperse light into a spectrum

blue is deviated more than red

Question 10

a diffraction grating

Answer 10

is typically used to separate or disperse the various wavelengths present

Question 11

Grating equation

Answer 11

sinθ(m) - sinθ(i) = mλ/a

incident angle = θ(i)
diffraction order angle = θ(m)

Question 12

Angular dispersion

Answer 12

D = dθ(m)/dλ = m/(acosθ(m))

Question 13

Instrumental Width

Answer 13

Δθ = λ/(Nacosθ(m))

Question 14

Free-Spectral Range

Answer 14

Δλ(FSR) = λ/m

Question 15

grating equation derivation

Answer 15

Δl = mλ = a(sinθ(m) - sinθ(i))

sinθ(m) - sinθ(i) = mλ/a

Question 16

Diffraction pattern

Answer 16

I = I(0) [(sin(Nφ/2))/(sin(φ/2))]^2

where φ = (2πa)/λ (sinθ(m) - sinθ(i))

Question 17

maxima occurs when

Answer 17

φ = 2πm

or sinθ(m) = mλ/a

Question 18

angular dispersion derivation

Answer 18

differentiating the grating equation with respect to wavelength

Question 19

linear dispersion derivation

Answer 19

x = Lθ

and dx/dλ = L dθ/dλ

substituting with the angular dispersion relation

Question 20

resolution limit

Answer 20

when the first minimum of λ(1) coincides with the maximum λ(2) (Rayleigh Criterion)

Question 21

Instrumental width is

Answer 21

the angular separation to the first minimum

Question 22

first minimum occurs

Answer 22

φ = 2π/N

N = number of grating lines

Question 23

Instrumental width derivation

Answer 23

differentiating, φ = (2πa)/λ (sinθ(m) - sinθ(i))

then substituting φ = 2π/N

Question 24

Resolution limit is

Answer 24

the minimum resolvable difference in wavelength Δλ corresponds to an angular seperation given by the instrumental width

Question 25

Resolving power derivation

Answer 25

instrumental width = angular dispersion

replacing angular dispersion for m/(acosθ(m))

then substituting λ/N = mΔλ

Question 26

Free spectral range is

Answer 26

the difference in wavelength for which you start to get an overlap of adjacent orders

Question 27

Free spectral range derivation

Answer 27

mλ’ = (m+1)λ

Δλ(FSR) = λ-λ’ = λ/m

Question 28

two sources of error associated with guide stars are

Answer 28

the cone effect

and

tip-tilt anisoplanatism

Question 29

spectroscopic instruments are

Answer 29

used to study the spectral content of light from astronomical objects