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  • Two coherent light sources A and B are at a distance from each other

Two coherent light sources A and B are at a distance \mathrm{3 \lambda} from each other \mathrm{(\lambda= wavelength).} The distances from \mathrm{A} on the X-axis at which the interference is constructive are:

Option: 1

\mathrm{3 \lambda}


Option: 2

\mathrm{8 \lambda}


Option: 3

\mathrm{5 \lambda / 4}


Option: 4

\mathrm{8.75 \lambda}


Answers (1)

best_answer

Say p be the point on X-axis, where constructive interference is obtained.

\mathrm{\mathrm{BP}-\mathrm{AP}=2 \lambda \text { or } \lambda}

\mathrm{\begin{aligned} & \therefore \sqrt{9 \lambda^2+\mathrm{x}^2}-\mathrm{x}=2 \lambda \\ & \therefore \quad 9 \lambda^2+\mathrm{x}^2=\mathrm{x}^2+4 \lambda^2+4 \mathrm{x} \lambda \Rightarrow \mathrm{x}=\frac{5 \lambda}{4} \end{aligned}}

\mathrm{\text { Further, } \sqrt{9 \lambda^2+\mathrm{x}^2}-\mathrm{x}=\lambda}

\mathrm{\begin{aligned} & \therefore \quad 9 \lambda^2+\mathrm{x}^2=\mathrm{x}^2+\lambda^2+2 \mathrm{x} \lambda \\ & \therefore \quad \mathrm{x}=4 \lambda \end{aligned}}

Posted by

Devendra Khairwa

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