Q.Two coherent sources of intensity I produce interference pattern. What will be the intensity where path difference is λ/6? (where λ = wavelength).

Phase difference (in radians) and path difference (in length units) are related by Δφ = (2π/λ)Δx.

A complete wave cycle (one full wavelength, λ, of path) corresponds to one complete phase cycle (2π radians). So a path difference of Δx corresponds to a phase difference that is the same FRACTION of 2π as Δx is of λ:

Δφ / 2π = Δx / λ

⟹ Δφ = (2π/λ) Δx

…

$I_{net}=I_1+I_2+2\sqrt{I_1I_2}\cos\phi$; at $\phi=\pi/2$ the cross term vanishes, leaving $I+4I=5I$.

Resultant intensity for two coherent waves of intensities $I_1,I_2$ with phase difference $\phi$:

$I = I_1+I_2+2\sqrt{I_1I_2}\cos\phi$ …