#### Two source S1 and S2 of intensity I1 and I2 are placed in front of a screen [Fig. 10.3 (a)]. The pattern of intensity distribution seen in the central portion is given by Fig. 10.3 (b). In this case which of the following statements are true. A. S1 and S2 have the same intensities. B. S1 and S2 have a constant phase difference. C. S1 and S2 have the same phase. D. S1 and S2 have the same wavelength.

The correct answers are the options (a, b, c)

Key concept:

For getting the sustained interference the initial phase difference between the interfering waves must remain constant, i.e., sources should be coherent.
for two coherent sources, the resultant intensity is given by
$I=I_1+I_2+2\sqrt{I_1I_2}\cos\phi$

Resultant intensity at the point of observation will be maximum.
$\\I_{max}=I_1+I_2+2\sqrt{I_1I_2}\\\\ I_{max}=\left ( \sqrt{I_1}+\sqrt{I_2} \right )^{2}$

Resultant intensity at the point of observation will be minimum.

$\\I_{min}=I_1+I_2-2\sqrt{I_1I_2}\\\\ I_{min}=\left ( \sqrt{I_1}-\sqrt{I_2} \right )^{2}$