Double-slit interference Wavelength

pattern of light intensity on screen light passing through 2 slits. labels on right refer difference of path lengths 2 slits, idealized here point sources.

when sinusoidal waveforms add, may reinforce each other (constructive interference) or cancel each other (destructive interference) depending upon relative phase. phenomenon used in interferometer. simple example experiment due young light passed through 2 slits. shown in figure, light passed through 2 slits , shines on screen. path of light position on screen different 2 slits, , depends upon angle θ path makes screen. if suppose screen far enough slits (that is, s large compared slit separation d) paths parallel, , path difference d sin θ. accordingly, condition constructive interference is:

d
sin
⁡
θ
=
m
λ
 
,


{\displaystyle d\sin \theta =m\lambda \ ,}

where m integer, , destructive interference is:

d
sin
⁡
θ
=
(
m
+
1

/

2
)
λ
 
.


{\displaystyle d\sin \theta =(m+1/2)\lambda \ .}

thus, if wavelength of light known, slit separation can determined interference pattern or fringes, , vice versa.

for multiple slits, pattern

i

q


=

i

1



sin

2


⁡

(



q
π
g
sin
⁡
α

λ


)


/


sin

2


⁡

(



π
g
sin
⁡
α

λ


)

 
,


{\displaystyle 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)\ ,}

where q number of slits, , g grating constant. first factor, i1, single-slit result, modulates more rapidly varying second factor depends upon number of slits , spacing. in figure i1 has been set unity, rough approximation.

it should noted effect of interference redistribute light, energy contained in light not altered, shows up.