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  4. Two light waves superimposing at the mid-point of the screen are coming from coherent sources of light with phase difference 3p rad. Their amplitudes are 1 cm each. The resultant amplitude at the given point will be,

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Q. Two light waves superimposing at the mid-point of the screen are coming from coherent sources of light with phase difference $3p$ rad. Their amplitudes are $1 \,cm$ each. The resultant amplitude at the given point will be,

Wave Optics

Solution:

Resultant amplitude,
$A = \sqrt{A_{1}^{2} +A_{2}^{2} + 2A_{1}A_{2} cos\, \phi} $
Here, $A_{1} = A_{2} = 1 \,cm, \phi = 3\pi \,rad $
$\therefore A = \sqrt{1^{2}+1^{2}+2\times 1\times 1\times cos \,3\pi} $
$= \sqrt{2+2\times\left(-1\right)} = 0$