Second: By displacing the source
After displacing the source
New optical path difference at po int M :
  = ( S S 2 M ) − ( S S1M ) = S S 2 + S 2 M − S S1 − S1M
  = ( S S 2 − S S1 ) + ( S 2 M − S1M )
But : ( S S 2 − S S1 ) =
Then :   =
ay
ax
and ( S 2 M − S1M ) =
d
D
ay ax
+
d D
𝑎𝑦
𝐼𝑓 𝑥 = 0 ⇒ =
𝑑
𝑇ℎ𝑒𝑛 𝑂 𝑖𝑠 𝑛𝑜𝑡 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑓𝑟𝑖𝑛𝑔𝑒.
𝑇ℎ𝑒𝑛 𝑡ℎ𝑒 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑓𝑟𝑖𝑛𝑔𝑒 𝑖𝑠 𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑑 𝑡𝑜 𝑛𝑒𝑤 𝑝𝑜𝑠𝑡𝑖𝑜𝑛 𝑂′ .
𝛿′
At po int O :  = 0. Then :
ay ax0
+
=0
d
D
yD
 x0 = −
d
The minus sign means: the displacement of the central fringe and
the displacement of the source have opposite directions