Sol. (i) The path difference,

S 2 P – OP = sin θ ,

S 1 P – OP = – sin θ ,

S 3 P – OP = sin θ ,

Fig.

The relative phases of the waves from S 1 , S 2 , S 3 when they interfere at P are

φ 1 = – , φ 2 = + , φ 3 =

As we are concerned with relative phases only, we can add φ 0 = + to φ 1 , φ 2 , φ 3 to simplify the calculations

= 0 = , = +

We use the phasor method to get resultant amplitude. Resultant amplitude at P,

A p = A + 2A cos

= A(1 + 2 cos φ )

Where φ = .

Fig.

Intensity at P, I p = (1 + 2 cos φ ) 2 I 0 … (i)

(ii) For a maximum/minimum at P, = O

1 + 2 cos φ = 0 (minimum)

cos φ = –

φ = 2n π ± or = 2n π ±

or d sin θ = λ for a minimum

and d sin θ = n λ λ for a maximum.