Question

In Young's double slit interference experiment, using two coherent sources of different amplitudes, the intensity ratio between bright to dark fringes is \(5 : 1\). The value of the ratio of resultant amplitudes of bright fringe to dark fringe is

• A. \((\frac{\sqrt{5}+1}{\sqrt{5}-1})\)
• B. \(\sqrt{5} : 1\)
• C. \((\frac{\sqrt{5}-1}{\sqrt{5}+1})\)
• D. \(1 : \sqrt{5}\)

Hint:

Intensity \(\propto\) amplitude\(^2\); use sum and difference of amplitudes.

Answer 1

The Correct Option is A

Concept:
\[ I \propto A^2 \] Step 1: Given ratio. \[ \frac{I_{\max}}{I_{\min}} = 5 \] \[ \frac{A_{\max}^2}{A_{\min}^2} = 5 \]
Step 2: Amplitude ratio. \[ \frac{A_{\max}}{A_{\min}} = \sqrt{5} \] For unequal amplitudes: \[ A_{\max} = a_1 + a_2, \quad A_{\min} = a_1 - a_2 \] \[ \frac{a_1 + a_2}{a_1 - a_2} = \frac{\sqrt{5}+1}{\sqrt{5}-1} \]
Step 3: Conclusion. Required ratio = \((\frac{\sqrt{5}+1}{\sqrt{5}-1})\)