Lab-4 blackbody and Filters (1)

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Name: 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