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  • Two source S_1 and S_2 of intensity I_1 and I_2 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.

Two sources 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 in 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.

Answers (1)

The correct answers are options a, b, and c.

Explanation:-

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

for a steady interference pattern to be formed, the phase difference between the two sources must remain constant. If the phase difference changes over time, the interference fringes would shift, and the pattern would not be stable.

The 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}

 

Posted by

Gurleen Kaur

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