Raw versus corrected
A raw reading of 250 with a background of 10 contains a corrected signal of 240. Doubling that source contribution gives 480, then adding the same background gives a new raw reading of 490.
SKILLS · QUANTITATIVE REASONING
Signal versus background
A detector reading can contain both a source signal and a baseline. A change in the source scales its contribution—not necessarily the whole reading.
01 · THE IDEA
Subtract the baseline, scale the signal, then add the appropriate baseline back.
New raw = new background + factor × (old raw − old background)
Use this model only when the detector is linear and the background is additive. If background changes between conditions, use each condition’s own background. For a point source without attenuation and with fixed detector geometry, signal is proportional to source power divided by distance squared.
Distance is squared
Doubling distance from an isotropic point source reduces its signal to one-quarter. An additive detector background does not fall to one-quarter unless the model says it changes too.
Know what is missing
If background is unknown or changes without measurement, a raw-reading ratio generally cannot determine the source-signal ratio. Do not assume that the baseline is zero.
CHANGE ONE PART OF THE MODEL
Keep the background separate
At baseline power and distance d, raw = 250 counts/s and background = 10 counts/s. The detector is linear, the point source is isotropic, and there is no attenuation.
Corrected signal240 counts/s
Fixed background10 counts/s
Raw reading250 counts/s
10 + (250 − 10) × 1 / 1² = 250 counts/s
The baseline is added once after the physical scaling is applied.
02 · WORKED EXAMPLES
Follow the setup, then the numbers
1. Change distance and power together
At distance d, raw signal is 250 counts/s with a constant background of 10 counts/s. Double both source power and distance, keeping the detector linear.
- Corrected original signal = 250 − 10 = 240 counts/s.
- Scaling factor = 2 / 2² = 1/2.
- New corrected signal = 120 counts/s.
- New raw signal = 120 + 10 = 130 counts/s.
Carry this forward: Scale 240, not 250. Source power and distance act on the source contribution.
2. Compare two conditions with different baselines
Condition A has raw = 180 and background = 30. Condition B has raw = 340 and background = 40, in the same units.
- Corrected A = 180 − 30 = 150.
- Corrected B = 340 − 40 = 300.
- Signal ratio B/A = 300/150 = 2.
Carry this forward: The raw ratio 340/180 would mix source change with baseline change.
03 · TRY IT IN DIFFERENT FORMS
Practice in different forms
For each question, identify the requested quantity and write the setup before calculating. Use a hint if needed, then choose an answer to see the explanation.
Untimed learning practice. These responses stay on this page and reset when you leave or reload; they do not change your test results.
QUESTION 1 / 4 · Across subjects
Double the source contribution
A linear detector reads 160 counts/s, including a fixed background of 40 counts/s. The source contribution doubles. What is the new raw reading?
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TAKE INTO A FRESH PASSAGE
Your setup checklist
- Identify whether the question asks for raw or corrected signal.
- Subtract the baseline appropriate to each condition.
- Apply source-power and distance factors to the corrected signal.
- Restore background only if the requested answer is a raw reading.
Before calculating, explain what each term represents and what the requested answer would mean.
Concept references
All scenarios and questions here are original learning exercises. These references support the underlying concepts; the simplified assumptions are stated within each example.