Lab-4 blackbody and Filters (1)
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Apr 3, 2024
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Lab - Blackbody Curves & UBV Filters
Background Material
Thoroughly review the “Spectra” and “Filters” background pages. The color index page may also
be helpful to review. Here the links:
http://astro.unl.edu/naap/blackbody/spectra.html
http://astro.unl.edu/naap/blackbody/filters.html
Filters Simulator Overview
The filters simulator allows one to observe light from various sources passing through multiple
filters and the resulting light that passes through to some detector. An “optical bench” shows the
source, slots for filters, and the detected light. The wavelengths of light involved range from 380
nm to 825 nm which more than encompass the range of wavelengths detected by the human eye.
The upper half of the simulator graphically displays the source-filter-detector process. A graph of
intensity versus wavelength for the source is shown in the leftmost graph. The middle graph
displays the combined filter transmittance – the percentage of light the filters allow to pass for
each wavelength. The rightmost graph displays a graph of intensity versus wavelength for the
light that actually gets through the filter and could travel on to some detector such as your eye or
a CCD. Color swatches at the far left and right demonstrate the effective color of the source and
detector profile respectively.
The lower portion of the simulator contains tools for controlling both the light source and the
filter transmittance.
∙
In the
source panel
perform the following actions to gain familiarity.
o
Create a
blackbody
source distribution – the spectrum produced by a light bulb
which is a continuous spectrum. Practice using the
temperature
and
peak height
controls to control the source spectrum.
o
Create a
bell-shaped
spectrum. This distribution is symmetric about a peak
wavelength. Practice using the peak
wavelength
,
spread
, and
peak height
controls to vary the source spectrum.
o
Practice creating
piecewise linear
sources. In this mode the user has complete
control over the shape of the spectrum as control points can be dragged to any
value of intensity.
▪
Additional control points are created whenever a piecewise segment is
clicked at that location.
▪
Control points may be deleted by holding down the Delete key and clicking
them.
▪
Control points can be dragged to any location as long as they don’t pass the
wavelength value of another control point.
∙
In the
filters panel
perform the following actions to gain familiarity.
NAAP – Blackbody Curves & UBV Filters 1/7
o
Review the shapes of the preset filters (the B, V, and R filters) in the
filters list
.
Clicking on them selects them and displays them in the graph in the
filters panel
.
o
Click the
add
button below the
filters list
.
▪
Rename the filter from the default (“filter 4”).
▪
Shape the piecewise linear function to something other than a flat line.
o
Click the
add
button below the
filters list
.
▪
Select
bell-shaped
from the
distribution type
pull down menu.
▪
Alter the features of the default and rename the filter.
o
If desired, click the
remove
button below the
filters list
. This removes the actively
selected filter (can’t remove the preset B, V, and R filters). Filters are not saved
anywhere. Refreshing the flash file deletes the filters.
Click (or copy/paste) here for simulator:
http://astro.unl.edu/naap/blackbody/animations/filters.html
Filters Simulator Questions
∙
Use the piecewise linear mode of the source panel to create a “flat white light” source at
maximum intensity. This source will have all wavelengths with equal intensity.
∙
Drag the V filter to a slot in the beam path (i.e. place them in the
filter rack
).
∙
Try the B and the R filter one at a time as well. Dragging a filter anywhere away from the
filter rack
will remove it from the beam path.
Question 1:
Sketch the graphs for the flat white light
and
V filter in the boxes below. What is the
effective color of the detected distribution?
Green
source distribution
combined filter transmittance
detected distribution
Question 2:
With the flat white light source, what is the relationship between the filter
transmittance and the detected distribution?
The plain white light doesn’t transmit when the
green light is added and the combined filter
transmittance graph and the detected distribution
graph are the same.
NAAP – Blackbody Curves & UBV Filters 2/7
∙
Add a new piecewise linear filter.
∙
Adjust the filter so that only large amounts of
green
light pass. This will require that
addition of points.
Question 3:
Use this green filter with the flat white light source and sketch the graphs below.
source distribution
combined filter transmittance
detected distribution
ACME Source FILTER RACK ACME Detector
Question 4:
Use the
blackbody
option in the
source panel
to create a blackbody spectrum that
mimics white light. What is the
temperature
of this blackbody you created?
6000k
∙
Add a new piecewise linear filter to the
filter list
.
∙
Modify the new filter to create a 40% “neutral density filter”. That is, create a filter which
allows
approximately
40%
of
the
light
to
pass
through
at
all
wavelengths
(
transmittance
)
∙
Set up the simulator so that light from the “blackbody white light” source passes through
this filter.
Question 5:
Sketch the graphs created above in the boxes below. (This situation crudely
approximates what sunglasses do on a bright summer day.)
source distribution
combined filter transmittance
detected distribution
Question 6:
Remove all filters in the filters rack. Place a B filter in the beam path with the flat
white light source (about 75% intensity). Then add a second B filter and then a third. Describe
and explain what happens when you add more than one of a specific filter.
By doing so, the
wavelengths get smaller and flatter and the color turns really dark.
NAAP – Blackbody Curves & UBV Filters 3/7
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Question 7:
Place a B filter in the beam path together with the 40% neutral density filter. Then
add a V filter into the beam path. Describe and explain what happens when you add more than
one filter to the filter rack.
When you add more than one filter to the filter rack, the wavelengths
disappear and there is no color.
purple filter profile
Question 8:
Create a piecewise linear filter that when used with the
flat white light source would allow red and blue wavelengths to pass
and thus effectively allowing
purple
light to pass. Draw the filter in
the box to the right.
FILTER RACK
∙
Remove all filters from the
filters rack
.
∙
Create a very narrow
bell-shaped
source distribution that is peaked at green wavelengths
(somewhere close to 550 nm). Notice the color!
∙
Expand the spread of the source distribution to maximum. Notice how the color changes.
∙
Change the distribution source to a
blackbody source
peaked at green wavelengths (a
temperature close to 5270 K). Again notice the color.
Question 9:
Using observations from the above actions, explain why we don’t observe “green
stars” in nature, though there are indeed stars which emit more green light than other
wavelengths.
By following the instructions, I think the reason we can see the green stars is
because the color might be shown in other colors. We just can't see it because it's so far away.
Close your applet. We are going to the next level, ready?
NAAP – Blackbody Curves & UBV Filters 4/7
Blackbody – Curves Mode Familiarization
The Blackbody Curve Simulator has two main modes – the
curves mode
and the
filters mode
. The
curves mode allows the exploration of blackbody curves including their peak wavelength and the
area under the curve which is related to their total energy production.
∙
Learn how to add and remove curves and change their temperatures.
o
Click the
add curve
button one or more times.
o
Change the temperature slider. Notice which curve changes.
o
Select a second curve and change temperature.
o
Remove all but 1 or 2 extra curves.
∙
Learn the
vertical scale
options. Have 2 or 3 curves in the explorer.
o
Change temperature with the
auto scale all curves
mode.
o
Change temperature with the
auto scale to selected curve
mode.
o
Change temperature with the
lock scales
mode.
∙
Learn the
horizontal scale
options. Select the horizontal scale tab.
o
Note how changing the rightmost limit changes the view.
∙
Use, if desired, the
indicate peak wavelength
and
highlight area under curve
options.
Here the link:
https://astro.unl.edu/nativeapps/
Question 10:
Create a blackbody curve of temperature
6000 K and
draw
the shape in the box to the right.
Does it have a peak? Is it symmetric about this peak?
Yes, it peaks at 483. This peak is not
symmetric.
______
__________________________________________
Question 11:
Create a second curve using the
add curve
button and use the temperature slider to
vary its temperature, chose one with 7000 K then move down to 5000 K. Can you find a
blackbody curve of another temperature that intersects the 6000 K curve at some wavelength?
, I
can't seem to find a blackbody curve of another temperature that intersects the 600k curve. I think
this is the same for two curves of any temperature.
________________________________________________________________________
NAAP – Blackbody Curves & UBV Filters 5/7
Question 12:
Make sure that there is only
one
curve and check
indicate peak wavelength
. Vary
the temperature of the curve and note how the peak wavelength changes. Formulate a general
statement relating the peak wavelength to temperature. Then compare this statement with Wien’s
Law discussed in your textbook.
The shorter the wavelength the less the peak is, and the higher
the temperature. Wien’s Law which says the temperature is inversely related to the peak
wavelength, so I think this just proves the law.
____ _ ______
Question 13:
Select the
highlight area under curve
option and lock the vertical scale. Vary the
temperature of the curve and note how the area under the curve changes. Formulate a general
statement relating the area under curve to temperature.
As the temperature increases the area
under the curve becomes smaller.
Question 14:
(Calculator Required) Complete the following table below. The “Area Ratio” is the
area for the curve divided by the area for the curve in the row above. This will tell you many
times greater the new ratio compared to the previous one.
Curve Temperature
Area Under Curve (W/m
2
)
Area Ratio
3000 K
4.59 x 10/6
.06244898
6000 K
7.35 x 10/7
.062288136
12000 K
1.18 x 10/9
.0627695
24000 K
1.88 x 10/10
Can you specify a more precise statement relating the area under the curve to temperature? Is this
consistent with what was referred to as the Stefan-Boltzmann Law in the background pages?
The hotter, the higher the curve . This does stay consistent with the Stefan Boltzmann law.
NAAP – Blackbody Curves & UBV Filters 6/7
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Blackbody Explorer – Filters Mode
The second mode is the
filters mode
and explores the use of UBVR filters with blackbody curves.
∙
Unselect
highlight area under curve
and
indicate peak wavelength
. Select the
filters
tab.
The light from a blackbody curve that passes through the UBVR filters are shown as colored
areas under the curve.
It is this area which is later translated into a number for color magnitude.
Remember that a magnitude is a logarithmic version of the flux (i.e. the amount of light) that
passes through a filter and that lower numbers reflect larger fluxes.
Note that this area depends
on both the source and the filter. What is listed as a V value is the apparent magnitude of a star
(assumed to blackbody which isn’t exactly true) through the V filter.
Question 15:
Vary the temperature and in the
table to the right note the temperature in at
which each filter peaks. Where are the filters
most sensitive, i.e. which temperature will give
the strongest response in a detector?
I believe R
is going to be the strongest response in a
detector.
Curve
Peak Temperature
U
8730
B
6650
V
5470
R
4850
Question 16: Use the color index feature to create a B-V index. This will compare the
apparent
magnitude of a star through the B filter to that through the V filter. Plot
temperature on the vertical axis and B-V on the horizontal.
Temperature
B-V
3000 K
1.65
4000 K
1.06
5000 K
.69
6000 K
.45
8000 K
.15
10,000 K
-.02
15,000 K
-.24
20,000 K
-.34
25,000 K
-.39
Question 17:
Use your graph to estimate the B-V value of a 12,000 K blackbody:
-.22
NAAP – Blackbody Curves & UBV Filters 7/7
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