MHT CET · Physics · Wave Optics
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
- A \(\left[\sqrt{\mathrm{I}_{1}}+\sqrt{\mathrm{I}_{2}}\right]^{2}\)
- B \(\mathrm{I}_{1}+\mathrm{I}_{2}\)
- C \(\left(\mathrm{I}_{1}+\mathrm{I}_{2}\right)^{2}\)
- D \(\mathrm{I}_{1}^{2}+\mathrm{I}_{2}^{2}\)
Answer & Solution
Correct Answer
(A) \(\left[\sqrt{\mathrm{I}_{1}}+\sqrt{\mathrm{I}_{2}}\right]^{2}\)
Step-by-step Solution
Detailed explanation
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 \(\mathrm{I}_{\max } \propto\left(\sqrt{\mathrm{I}}_{1}+\sqrt{\mathrm{I}}_{2}\right)^{2}\)
\(\mathrm{I} \propto \mathrm{a}^{2}\)
\(\therefore \sqrt{\mathrm{I}} \propto \mathrm{a}\)
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 \(\mathrm{I}_{\max } \propto\left(\sqrt{\mathrm{I}}_{1}+\sqrt{\mathrm{I}}_{2}\right)^{2}\)
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