Question

Two coherent light sources of intensity ratio $n$ are employed in an interference experiment. The ratio of the intensities of the maxima and minima in the interference pattern is $(I_1>I_2)$

• A. $\left(\dfrac{n+1}{n-1}\right)^2$
• B. $\left(\dfrac{\sqrt{n}+1}{\sqrt{n}-1}\right)^2$
• C. $\dfrac{\sqrt{n}+1}{\sqrt{n}-1}$
• D. $\dfrac{n+1}{n-1}$

Hint:

Always use amplitudes (square roots of intensities) when dealing with interference maxima and minima.

Answer 1

The Correct Option is B

Step 1: Write expressions for maximum and minimum intensities.
For two coherent sources with intensities $I_1$ and $I_2$: \[ I_{\max} = (\sqrt{I_1} + \sqrt{I_2})^2 \] \[ I_{\min} = (\sqrt{I_1} - \sqrt{I_2})^2 \] Step 2: Use given intensity ratio.
Given: \[ \dfrac{I_1}{I_2} = n \Rightarrow \dfrac{\sqrt{I_1}}{\sqrt{I_2}} = \sqrt{n} \] Step 3: Find ratio of maxima to minima.
\[ \dfrac{I_{\max}}{I_{\min}} = \left(\dfrac{\sqrt{n}+1}{\sqrt{n}-1}\right)^2 \]