Question

Two waves of intensity $ I $ undergo interference. The maximum intensity obtained is:

• A. $ \frac{I}{2} $
• B. $ I $
• C. $ 2I $
• D. $ 4I $

Answer 1

Answer: (D)

When two interfering waves meet in the same phase, resultant intensity is maximum. The resultant intensity due to two waves
$ {{I}_{1}} $ and $ {{I}_{2}} $
and having phase difference
$ \phi $ between them is given by
$ I={{I}_{1}}+{{I}_{2}}+2\sqrt{{{I}_{1}}{{I}_{2}}}\cos \phi $
For maximum intensity, $ \phi =0 $
$ \therefore $ $ {{I}_{\max }}={{(\sqrt{{{I}_{1}}}+\sqrt{{{I}_{2}}})}^{2}} $
Given, $ {{I}_{1}}={{I}_{2}}=I $
$ \therefore $ $ {{I}_{\max }}={{(\sqrt{I}+\sqrt{I})}^{2}}=4I $
Maximum intensity is also known as constructive interference.