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When waves from two
coherent sources, having amplitudes \( a \) and \( b \) superimpose, the amplitude \( R \) of the resultant wave is given by \( R=\sqrt{a^{2}+b^{2}+2 a b \cos \phi} \), where \( \phi \) is the constant phase angle between the two waves. The resultant intensity \( I \) is directly proportional to the square of the amplitude of the resultant wave, that is, \( I \propto R^{2} \), that is, \( I \propto\left(a^{2}+b^{2} 2 a b \cos \phi\right) \). For constructive interference, \( \phi=2 n \pi \) and \( I_{\max }=(a+b)^{2} \). For destructive interference, \( \phi=(2 n-1) \phi \) and \( I_{\min }=(a-b)^{2} \). If \( I_{1}, I_{2} \) are intensities of light from two slits of widths \( \omega_{1} \) and \( \omega_{2}, I_{1} / I_{2}=\omega_{1} / \omega_{2}=a^{2} / b^{2} \). Light waves from two coherent sources of intensity ratio \( 81: 1 \) produce interference.
The ratio of amplitudes of light waves from two sources is
(A) \( 1: 4 \)
(B) \( 4: 1 \)
(C) \( 2: 1 \)
(D) \( 1: 2 \)
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