From the double slit experiment we get to know that
Path difference = S2P – S1P
\(\begin{array}{l}sqrt{(D^{2}+d^{2})-D}\end{array} \)
=
\(\begin{array}{l}D(1+frac{1}{2}frac{d^{2}}{D^{2}}-1)\end{array} \)
=
\(\begin{array}{l}frac{d^{2}}{2D}\end{array} \)
=
\(\begin{array}{l}Delta x=frac{d^{2}}{2times 10d}\end{array} \)
=
\(\begin{array}{l}frac{d}{20}\end{array} \)
=
\(\begin{array}{l}frac{5lambda }{20}\end{array} \)
=
\(\begin{array}{l}frac{lambda }{4}\end{array} \)
=
\(\begin{array}{l}Delta phi =frac{2Pi }{lambda } times frac{lambda }{4}=frac{pi }{2}\end{array} \)
The intensity at the desired point will be
I=I0cos2(ϕ/2)=I0cos2(π/4)=I0/2
Answer
I0/2
