Path Difference Decides Fringes

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

If the path difference is not a whole number of wavelengths, the point is neither a bright fringe center nor fully constructive, so the bright label is rejected. The test is exact only against the stated wavelength and integer rule. Real fringes have finite visibility, bandwidth, and alignment error, so the bright/dark boundary is measured with uncertainty rather than read off cleanly.

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