Ratio of intensities between a point A and that of central fringe is 0.853. Then path difference between two waves at point A will be

$\frac{\lambda}{2}$ $\frac{\lambda}{4}$ $\frac{\lambda}{8}$ $\lambda$

$\frac{\lambda}{8}$

$R^2=a^2+b^2+2 a b \cos \phi$ $\frac{I_R}{I_{\max }}=0.853$ ∴ $I_R=0.853 ~I_{\max }=0.853 \times 4 I$ $I_R=I+I_0+2 I \cos \phi=2 I(1+\cos \phi)=0.853 \times 4 I$ $\Rightarrow \phi=\frac{\pi}{4}=\frac{\lambda}{8}$