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

$\frac{λ}{8}$

$R^2 = a^2 + b^2 + 2ab\, \cos\phi$

$\frac{I_R}{I_{max.}}=0.853$

$∴I_R =0.853\, I_{max} = 0.853×4I$

$I_R = I + I_0 + 2I\, \cos\phi = 2I (1 + \cos\phi) =0.853 ×4I$

$⇒\phi=\frac{π}{4}=\frac{λ}{8}$