Editing Wavelength (section)

=== Double-slit interference ===
{{Main|Interference (wave propagation)}}

[[File:Interferometer path differences.JPG|thumb|Pattern of light intensity on a screen for light passing through two slits. The labels on the right refer to the difference of the path lengths from the two slits, which are idealized here as point sources.]]

When sinusoidal waveforms add, they may reinforce each other (constructive interference) or cancel each other (destructive interference) depending upon their relative phase. This phenomenon is used in the [[Interferometry|interferometer]]. A simple example is an experiment due to [[Thomas Young (scientist)|Young]] where light is passed through [[Double-slit experiment|two slits]].<ref name=Sluder>
{{cite book
 |title=Digital microscopy
 |author1=Greenfield Sluder  |author2=David E. Wolf
 |name-list-style=amp |url=https://archive.org/details/digitalmicroscop00gree
 |url-access=registration
 |page=[https://archive.org/details/digitalmicroscop00gree/page/15 15]
 |chapter=IV. Young's Experiment: Two-Slit Interference
 |isbn=978-0-12-374025-0
 |edition=3rd
 |year=2007
 |publisher=Academic Press
 }}</ref>
As shown in the figure, light is passed through two slits and shines on a screen. The path of the light to a position on the screen is different for the two slits, and depends upon the angle θ the path makes with the screen. If we suppose the screen is far enough from the slits (that is, ''s'' is large compared to the slit separation ''d'') then the paths are nearly parallel, and the path difference is simply {{nowrap|''d'' sin ''θ''}}. Accordingly, the condition for constructive interference is:<ref name=Halliday>
{{cite book
 |title=Fundamentals of Physics
 |chapter-url=https://books.google.com/books?id=RVCE4EUjDCgC&pg=PT965
 |page=965
 |chapter=§35-4 Young's interference experiment
 |last1=Halliday|last2=Resnick|last3=Walker
 |isbn=978-81-265-1442-7
 |year=2008
 |edition=Extended 8th
 |publisher=Wiley-India
 }}</ref>
<math display="block"> d \sin \theta = m \lambda \ , </math>
where ''m'' is an integer, and for destructive interference is:
<math display="block"> d \sin \theta = (m + 1/2 )\lambda \ . </math>

Thus, if the wavelength of the light is known, the slit separation can be determined from the interference pattern or ''fringes'', and ''vice versa''.

For multiple slits, the pattern is<ref name=Harris>
{{cite book |author=Kordt Griepenkerl|title=Handbook of physics |chapter-url=https://books.google.com/books?id=c60mCxGRMR8C&pg=PA307 |pages=307 ''ff'' |editor1=John W Harris |editor2=Walter Benenson |editor3=Horst Stöcker |editor4=Holger Lutz |chapter= §9.8.2 Diffraction by a grating |isbn=0-387-95269-1 |year=2002 |publisher=Springer}}
</ref>
<math display="block">I_q = I_1 \sin^2 \left( \frac {q\pi g \sin \alpha} {\lambda} \right)  /  \sin^2  \left( \frac{ \pi g \sin \alpha}{\lambda}\right) \ , </math>
where ''q'' is the number of slits, and ''g'' is the grating constant. The first factor, ''I''<sub>1</sub>, is the single-slit result, which modulates the more rapidly varying second factor that depends upon the number of slits and their spacing. In the figure ''I''<sub>1</sub> has been set to unity, a very rough approximation.

The effect of interference is to ''redistribute'' the light, so the energy contained in the light is not altered, just where it shows up.<ref name= Murphy>
{{cite book
 |title=Fundamentals of light microscopy and electronic imaging
 |url=https://books.google.com/books?id=UFgdjxTULJMC&pg=PA64
 |page=64
 |author= Douglas B. Murphy
 |isbn=0-471-23429-X
 |year=2002
 |publisher=Wiley/IEEE
 }}</ref>