Two coherent sources of intensities $\mathrm{l}_{1}$ and $\mathrm{I}_{2}$ produce an interference pattern on…

Two coherent sources of intensities $\mathrm{l}_{1}$ and $\mathrm{I}_{2}$ produce an interference pattern on screen. The maximum intensity in the interference pattern is
  1. $\left[\sqrt{\mathrm{I}_{1}}+\sqrt{\mathrm{I}_{2}}\right]^{2}$
  2. $\mathrm{I}_{1}+\mathrm{I}_{2}$
  3. $\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right)^{2}$
  4. $\mathrm{I}_{1}^{2}+\mathrm{I}_{2}^{2}$

Solution

Intensity is proportional to square of the amplitude. $\mathrm{I} \propto \mathrm{a}^{2}$ $\therefore \sqrt{\mathrm{I}} \propto \mathrm{a}$ Maximum intensity is produced when the two amplitudes get added (phase difference is $2 n \pi$ ). $\therefore \mathrm{I}_{\max } \propto\left(\mathrm{a}_{1}+\mathrm{a}_{2}\right)^{2} \quad$ or $\mathrm{I}_{\max } \propto\left(\sqrt{\mathrm{I}}_{1}+\sqrt{\mathrm{I}}_{2}\right)^{2}$

Asked in: MHT CET 2020 (14 Oct Shift 1)

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