The correct option is
C D=15λ4
The maximum and minimum path difference between the waves are,
2λ (when point
P is very close to
S2) and zero (when point
P is at infinity), respectively.
For any minima, the path difference is equal to odd multiple of
λ2.
∴ Only two minima obtained from
S2 till infinity, along the line
S2P.
Close to
S2, the path difference is
2λ. As we move away from
S2, along the line
S2P, the path difference starts to decrease.
∴ The farthest minima will have a path difference
λ/2 and the nearest minima will have a path difference of
3λ2.
Now, for the farthest minima,
S1P−S2P=λ2
⇒√4λ2+D2−D=λ2
4λ2+D2=(D+λ2)2
⇒4λ2+D2=λ24+D2+Dλ
⇒D=4λ−λ/4=15λ4
Hence,
(C) is the correct answer.