Double-Slit Interference: Fringe Positions and Maximum Order

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Path difference in a double-slit experiment

The difference between the distances traveled by the two waves to the same observation point.

Constructive interference

Waves reinforce when their path difference is an integer multiple of the wavelength: $d\sin\theta=m\lambda$.

Destructive interference

Waves tend to cancel when their path difference is a half-integer multiple of the wavelength: $d\sin\theta=(m+1/2)\lambda$.

Fringe order

The integer $m$ that labels a bright fringe; the central bright fringe has order zero.

Wavelength from a bright-fringe angle

For a bright fringe with nonzero order, calculate wavelength using $\lambda=d\sin\theta/m$.

Quiz questions

1. Which condition gives a bright fringe in a double-slit pattern?Answer: $d\sin\theta=m\lambda$, where $m$ is an integer.
2. Which condition gives a dark fringe in a double-slit pattern?Answer: $d\sin\theta=(m+1/2)\lambda$, where $m$ is an integer.
3. Slits separated by $0.0100\,\text{mm}$ produce a third-order bright fringe at $10.95^\circ$. What is the wavelength?Answer: $633\,\text{nm}$
4. If $d/\lambda=15.8$, what is the greatest possible integer order of a constructive fringe?Answer: $15$
5. What is the order of the central bright fringe in a double-slit pattern?Answer: $m=0$