A) the intensities at the screen due to two slits are 5 units and 4 units respectively
B) the intensities at the screen due to the two slits are 4 units and 1 units, respectively
C) the amplitude ratio is 7
D) the amplitude ratio is 6
Correct Answer: B
Solution :
Given, \[\frac{{{I}_{\max }}}{{{I}_{\min }}}=9=\frac{{{({{a}_{1}}+{{a}_{2}})}^{2}}}{{{({{a}_{1}}-{{a}_{2}})}^{2}}}\] \[\therefore \] \[\frac{{{a}_{1}}+{{a}_{2}}}{{{a}_{1}}-{{a}_{2}}}=3\] or \[2{{a}_{1}}=4{{a}_{2}}\] or \[{{a}_{1}}=2{{a}_{2}}\] \[\Rightarrow \] \[\frac{{{a}_{1}}}{{{a}_{2}}}=2\] Again, intensity ratio at the screen due to two silts \[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{a_{1}^{2}}{a_{2}^{2}}=\frac{4}{1}\] Hence, amplitude ratio is 2 and intensities at the screen due to two slits are 4 units and 1 units, respectively.
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