With the same matched line, three calibration scales move the displayed detector channel.

With the same matched line, three calibration scales move the displayed detector channel. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Scale changes the detector channel

The photon energy stays 5 joules and the offset stays 1 channel. Scale 1 maps the line to channel 6.

channel=1⋅5+1=5+1=6channel=1\cdot 5 + 1=5 + 1=6
Calibration scale scanThe same line moves when the channel scale changes.E=5 Jchannel=6scale=1

Scale changes the detector channel

The photon energy stays 5 joules and the offset stays 1 channel. Scale 2 maps the line to channel 11.

channel=2⋅5+1=10+1=11channel=2\cdot 5 + 1=10 + 1=11
Calibration scale scanThe same line moves when the channel scale changes.E=5 Jchannel=11scale=2

Scale changes the detector channel

The photon energy stays 5 joules and the offset stays 1 channel. Scale 3 maps the line to channel 16.

channel=3⋅5+1=15+1=16channel=3\cdot 5 + 1=15 + 1=16
Calibration scale scanThe same line moves when the channel scale changes.E=5 Jchannel=16scale=3