**Expression for bandwidth**

Let d be the distance between two coherent sources A and B of wavelength λ. A screen XY is placed parallel to AB at a distance D from the coherent sources. C is the mid point of AB. O is a point on the screen equidistant from A and B. P is a point at a distance x from O, as shown in Figure. Waves from A and B meet at P in phase or out of phase depending upon the path difference between two waves.

**Fig: Interference band width**

Draw AM perpendicular to BP

The path difference δ = BP – AP

AP = MP

**∴ δ = BP – AP = BP – MP = BM**

In right angled Δ ABM, BM = d sin θ

If θ is small, sin θ = θ

∴ The path difference δ = θ.d

In right angled triangle COP, tan θ = OP/ CO = x/D

For small values of θ, tan θ = θ

∴ **The path difference δ = xd/D**