Theory of Young’s Double slits Formula
1st Subsidiary
max = P
P
w
S2
M
S1
O (central
max)
Q
Double slits
D



Screen
The two triangles S1S2Q and MOP are similar (if we make the assumption that
D >> w or s).
S1 Q
OP
Therefore we get the following ratio:
=
S1 S2
OM
If P is the first subsidiary maximum then S1Q = λ, also OP = fringe separation
w and S1S2 = slit separation s, OM = distance from slits to screen D. This
gives:
Key equation:
Or
λ
=
sw
D
D
w
=
λD
s
Typical values:




D = distance from the slits to the screen (1 - 10m for laser),
w = separation between adjacent fringes,
s = separation of the twin slits (typically ~ 0.2 - 0.3mm)
λ = wavelength of laser light
Note: If D is not much greater than w or s, use the path difference method (i.e. with microwaves)