Question 8: create a piecewise linear filter that when used with the

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Blackbody Curves & UBV Filters – Student Guide

Background Material

Thoroughly review the “Spectra” and “Filters” background pages. The color index page may also

be helpful to review.

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.

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In the source panel perform the following actions to gain familiarity.

o Create an 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.

NAAP – Blackbody Curves & UBV Filters 1/7•

In the filters panel perform the following actions to gain familiarity.

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.

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?

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?

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

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?

• 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.

• 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. 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.

NAAP – Blackbody Curves & UBV Filters 3/7Question 7: Place a B filter in the beam path 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.

purple filter

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.

• 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 an 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.

NAAP – Blackbody Curves & UBV Filters 4/7Blackbody – 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.

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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.

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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.

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Learn the horizontal scale options. Select the horizontal scale tab.

o Note how changing the rightmost limit changes the view.

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Use, if desired, the indicate peak wavelength and highlight area under curve options.

Blackbody Curves – Questions

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?

Question 11: Create a second curve using the add curve button and use the temperature slider to

vary its temperature. Can you find a blackbody curve of another temperature that intersects the

6000 K curve? Do you believe this would be true for two curves of any temperature?

NAAP – Blackbody Curves & UBV Filters 5/7Question 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 the background pages.

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.

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 is compared to the previous one.

Curve Temperature

Area Under Curve (W/m 2 )

Area Ratio

3000 K

6000 K

12000 K

24000 K

Can you specify a more precise statement relating the area under curve to temperature. Is this

consistent with what was referred to as the Stefan-Boltzmann Law in the background pages?

NAAP – Blackbody Curves & UBV Filters 6/7Blackbody Explorer – Filters Mode

The second mode is the filters mode and explores the use of UBVR filters with blackbody

curves.

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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 Curve

U

the filters most sensitive, i.e. which temperature will give the B

strongest response in a detector? V

Peak Temperature

R

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

3000 K

B-V

4000 K

5000 K

6000 K

8000 K

10,000 K

15,000 K

20,000 K

25,000 K

Question 17: Use your graph to estimate the B-V value of a 12,000 K blackbody.

NAAP – Blackbody Curves & UBV Filters 7/7