Q148 / 180 · COMEDK 2023 (Memory Based) · Physics

In Young's double slit interference experiment, using two coherent waves of different amplitudes, the intensities ratio between bright and dark fringes is 3 . Then, the value of the ratio of the amplitudes of the wave that arrive there is

  • Correct answer
    A
    $\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)$
  • B
    $\left(\frac{\sqrt{3}-1}{\sqrt{3}+1}\right)$
  • C
    $\sqrt{3}: 1$
  • D
    $1: \sqrt{3}$

Solution

$\begin{aligned} & \text { Here, } \frac{I_{\text {bright }}}{I_{\text {dark }}}=\frac{I_{\max }}{I_{\min }}=3 (given) \\ & \Rightarrow \quad \frac{\left(a_1+a_2\right)^2}{\left(a_1-a_2\right)^2}=\frac{3}{1} \Rightarrow \frac{a_1+a_2}{a_1-a_2}=\sqrt{3} \\ & \Rightarrow \quad a_1+a_2=\sqrt{3}\left(a_1-a_2\right) \Rightarrow \frac{a_1}{a_2}=\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right) \end{aligned}$

Hence, the correct answer is option: 'A'.

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