Question 309: Wave Optics

Question

The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is $9: 1$. The intensities of the light sources used are in the ratio

Accepted Answer

To determine the intensity ratio of the light sources in an interference pattern, we start with the given intensity ratio of maxima to minima, which is 9:1. This relationship is expressed as:
$ \frac{I_{\max }}{I_{\min }} = \frac{\left(\sqrt{I_1}+\sqrt{I_2}\right)^2}{\left(\sqrt{I_1}-\sqrt{I_2}\right)^2} $
Plugging the given ratio into the equation:
$ \frac{9}{1} = \frac{\left(\sqrt{I_1}+\sqrt{I_2}\right)^2}{\left(\sqrt{I_1}-\sqrt{I_2}\right)^2} $
Taking the square root on both sides of the equation gives:
$ \frac{3}{1} = \frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}} $
Cross-multiplying to solve for the intensity terms:
$ 3\left(\sqrt{I_1}-\sqrt{I_2}\right) = 1\left(\sqrt{I_1}+\sqrt{I_2}\right) $
Expanding and rearranging terms, we have:
$ 3 \sqrt{I_1} - 3 \sqrt{I_2} = \sqrt{I_1} + \sqrt{I_2} $
Rearranging terms gives:
$ 2 \sqrt{I_1} = 4 \sqrt{I_2} $
Solving for the square root ratio, we find:
$ \sqrt{\frac{I_1}{I_2}} = \frac{2}{1} $
Squaring both sides provides the ratio of intensities:
$ \frac{I_1}{I_2} = \frac{4}{1} $
Therefore, the ratio of the intensities of the light sources is $4:1$.

Answer

$3: 1$

Answer

$4: 1$

Answer

$9: 1$

Answer

$10: 1$

Wave Optics

The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is 9: 1. The intensities of the light sources used are in the ratio

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