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 is proportional to the square of the amplitude, and bright and dark fringes correspond to the sum and difference of the two amplitudes.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For two coherent sources with amplitudes \(a_1\) and \(a_2\), the bright fringe has resultant amplitude \(a_1+a_2\) and the dark fringe has \(a_1-a_2\).
Intensity is proportional to the square of the amplitude.

Step 2: Set up the ratio
\(\dfrac{I_{max}}{I_{min}}=\dfrac{(a_1+a_2)^2}{(a_1-a_2)^2}=\dfrac{5}{1}\)

Step 3: Take the square root
\(\dfrac{a_1+a_2}{a_1-a_2}=\sqrt{5}\)
This is exactly the ratio of the resultant amplitude of the bright fringe to that of the dark fringe.

Step 4: Compare the options
The ratio is \(\sqrt{5} : 1\), which matches the second option.

Final Answer:
The ratio of resultant amplitudes of bright to dark fringe is \(\sqrt{5} : 1\). \[ \boxed{\text{(B) }\sqrt{5} : 1} \]