Lecture 8: Spectroscopic Instruments

Question 1

chemical composition of stellar body can be

Answer 1

determined by observing its spectrum

Question 2

velocity determined from

Answer 2

doppler shift of spectral lines

Question 3

doppler shift observed in light from stars

Answer 3

determine rotation frequency of arms of a spiral galaxy

large planets cause stars to wobble leading to a doppler shift

Question 4

common components of spectroscopic instruments

Answer 4

slit
collimator
diffraction grating
focusing mirror
detector

Question 5

in general, spectroscopic instruments

Answer 5

map wavelength to position on detector

Question 5

resolving power

Answer 5

R= lambda / delta lambda

Question 6

spectrometer

Answer 6

also ‘monochrometer’
entrance and exit slits
tune wavelength by rotating grating

Question 7

spectrograph

Answer 7

also ‘spectroscope’
entrance slit
spectrum recorded on camera or CCD array

Question 8

diffraction gratings - light transmitted by

Answer 8

gaps between lines - apertures

each acts as an independent source

Question 9

diffraction gratings- secondary wavelets (circular waves) emanate from

Answer 9

each gap

Question 10

diffraction grating - constructive interference at

Answer 10

certain angles (diffraction orders)

Question 11

diffraction angle depends on

Answer 11

wavelength

Question 12

grating equation

Answer 12

sin thetam - sin thetai = m lambda/a

Question 13

angular dispersion equation

Answer 13

D= dthetam/d lambda = m/a cos thetam

Question 14

instrumental width equation

Answer 14

delta theta = lambda / Na cos theta m

Question 15

resolving power equation

Answer 15

R=lambda / delta lambda = mN

Question 16

free spectral range equation

Answer 16

delta lambda_FSR = lambda/m

Question 17

intensity maxima occur at

Answer 17

diffraction angles when the path length difference is equal to an integer number of wavelengths

Question 18

angular dispersion of the grating is the

Answer 18

rate at which the angle changes with wavelength

Question 19

angular dispersion is derived by

Answer 19

differentiating the grating equation with respect to wavelength

Question 20

getting from angular to linear dispersion

Answer 20

small angle approx x=Ltheta

dx/dlambda = L d theta/dlambda
sub in angular dispersion

Question 21

limit of resolution is when

Answer 21

first min of lambda1 coincides with the max of lambda 2

rayleigh criterion

Question 22

instrumental width delta theta

Answer 22

angular separation to the first min

Question 23

first min occurs for a phase

Answer 23

thi = 2pi/N

Question 24

min resolvable difference in wavelength corresponds to

Answer 24

an angular separation given by the instrumental width

Question 25

resolving power derivation

Answer 25

equation instrumental width and angular dispersion

Question 26

at high orders, the spectra

Answer 26

start to overlap blue from higher order overlaps with red from lower order

Question 27

free spectral range is

Answer 27

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

Question 28

constructive interference where phase difference between adjacent rulings is

Answer 28

an integer multiple of 2pi

Question 29

0th order is

Answer 29

direct reflection from surface or specular reflection

Question 30

grating is described mathematically as a

Answer 30

convolution of a single slit of width b with an array of delta functions spaced apart by a

Question 32

diffraction pattern is fourier transform of

Answer 32

grating transfer function (by convolution theorem in product of fourier transforms of the individual funcs)

Question 33

intensity maximum at

Answer 33

zeroth order falls off going away from zeroth order

Question 34

reflection grating inefficient

Answer 34

most light directed to 0th order which is undispersed and not useful only around 10% at 1st order need some means of directing all light to order of interest