Path Difference Decides Fringes

wrong-path-difference-rejects-a-bright-label

The bright label is rejected when the checked path difference does not match the wavelength ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The measured difference is between bright rows

The exact path difference is 5 m. It sits between the two neighboring integer-wavelength bright rows.

Δ=15 m−10 m=5 m\Delta=15\ \text{m} - 10\ \text{m} = 5\ \text{m}
Measured mismatchThe path ledger is still valid even when the label is rejected.path Apath BpathA=10 mpathB=15 mpathDifference=5 mwavelength=2 morder=2 counthalfWaveBit=0 bitmode=brightacceptedBit=0 bit

Neighboring integer rows would be accepted

A wrong row is not close enough. The rows on either side are accepted because they are exact integer wavelength counts; the middle row is rejected.

Δλtargetaccepted4 m2 m215 m2 m206 m2 m31\begin{array}{c|c|c|c}\Delta&\lambda&\text{target}&\text{accepted}\\4\ \text{m}&2\ \text{m}&2&1\\5\ \text{m}&2\ \text{m}&2&0\\6\ \text{m}&2\ \text{m}&3&1\\\end{array}

A nonmatching path difference rejects the bright label

The diagram still shows the path lengths, but the accepted bit stays at 0.

Δ=5 m≠2λ=4 m;accepted=0\Delta=5\ \text{m}\ne2\lambda=4\ \text{m};\quad \text{accepted}=0
Rejected bright path ledgerA same-caption bright claim fails when the exact path difference is wrong.path Apath BpathA=10 mpathB=15 mpathDifference=5 mwavelength=2 morder=2 counthalfWaveBit=0 bitmode=brightacceptedBit=0 bit