Two Sources \(S_1\) and \(S_2 \) of intensity \(I_1\) and \(I_2\) are in front of a screen [Fig.(a)]. The pattern of intensity distribution seen in the central portion is given by Fig.(b).


In this case, which of the following statements are true?

 
(a)  \(S_1\) and \(S_2\) have the same intensities.
(b)  \(S_1\) and \(S_2\) have a constant phase difference.
(c)  \(S_1\) and \(S_2\) have the same phase.
(d)  \(S_1\) and \(S_2\) have the same wavelength. 

Choose the correct option:

1. (a), (b), (c) 2. (a), (b), (d)
3. (b), (c), (d) 4. (c), (d)

(a, b, d) Hint: The interference occurs when the sources are coherent sources.
Consider the pattern of the intensity shown in the figure.

Step 1: Find the comparative intensities of the sources.

(i) As intensities of all successive minima are zero, hence we can say that two sources S1and S2 are having the same intensities.

Step 2: Find the phase difference of the sources.

(ii) As the width of the successive maxima (pulses) increases in a continuous manner, we can say that the path difference (x) or phase difference varies in a continuous manner.

Step 3: Find the comparative wavelengths of the sources.

(iii) We are using monochromatic light in YDSE to avoid overlapping and to have a very clear pattern on the screen.