# Astronomy 302

# Lecture 14

# Spectra

## 1.0 Light can be dispersed into colors

White light is really the sum of many different
frequencies.

We can use a dispersing element to analyze the amount/intensity
of
light at each wavelength (this is called a spectrum)

a nice image of prism from here

The reason a spectrum is made is due to light slowing down in
the
denser glass so it must take a more direct route. This is know
as
Snell's law

Snell's Law: *n*_{1}sin*θ*_{1}
= *n*_{2}sin*θ*_{2
so as we can see how Snell's law applies to a prism. from
here
This shows that since n is a function of lambda
we get a
spectrum! from
here
this site has nice images for basic optics
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## 2.0 Dispersion grating

While prisms are fine for very low resolution spectra in
astronomy we usually need higher spectral resolutions.

In optics,
a **diffraction grating** is a reflecting or transparent element, whose
optical
properties are periodically modulated. Most commonly the
diffraction
gratings are realized as fine parallel and equally spaced
grooves or
*rulings* on material surface. When light is incident on a
diffraction grating, diffractive and mutual interference*diffraction orders*.
Because of their dispersive properties,
gratings are
commonly used in monochromators and spectrometers.

a cartoon of a transmission grating from here

A typical reflective diffraction grating from here

what are these orders physically? -- constructive interference!

one way of thinking about these orders from
here

2.1 The grating Equation

where: n is the order of diffraction, λ is the diffracted
wavelength d
is the grating constant (the distance between successive
grooves) θi is
the angle of incidence measured from the normal and θd is the
angle of
diffraction measured from the normal.

The diagram above shows the orders of the diffracted wavelength.
As
well as positive orders, light can also be diffracted in the
opposite
direction (i.e. n = -1, -2 etc.) Higher orders may also appear
but
these decrease in intensity. Usually the first order lines (n=1
or
n=-1) are the most intense.

## 3.0 Spectrographs

Once we have a grating we need to use a spectrograph to
produce a spectrum

A more "real" design looks like that below from the Carbon
Observatory satellite

SLITS --- why do we need them?

By use of slit we can keep light from the seeing disk from
overlapping from
here

The end result is a nice spectrum

See
this
site for background on stellar spectra

the spectra of stars look like

This is how astronomers classify different stellar types (in
order of
decreasing effective temp)

Usually astronomers only plot the spectra as lines

from here

## 4.0 Spectrographs

What does the spectra really look like on our CCD?

Clearly a lot of processing is required before we can extract

the spectrum. Compare to the calibrated B5V spectrum above...

RESOLUTION of a Spectrograph

R = Lambda / Delta_Lambda = c/Delta_v

where Delta Lambda is the smallest difference the spectrograph
can resolve

and c = speed of light, and Delta_v is the smallest velocity
difference that can be measured.

example

(STIS) can distinguish features 0.17 nm apart at a wavelength of
1000 nm, giving it a resolution of 0.17 nm and a
resolving power of about 5,900

The STIS example above then
has a spectral resolution of 51 km/s.

5.0 SPECTROGRAPH DESIGN (lecture 15)

see here for the rest of the
lecture
on spectrograph design

from Dennis Zaritsky's lecture.

6.0 SPECTRAL DATA REDUCTION (lecture 16)

See here for notes on how IRAF can
reduce
spectroscopic data

(lecture notes from M. Bote lick obs.)

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