Question

two coherent light sources of intensities ratio 36:9 are employed in an interference experiment. what is the ratio of the intensities of the maxima and minima​

Answer 1

The ratio of the intensities of the maxima and minima​ = 9:1.

• Natural occurrences like interference take occuring everywhere and all the time. However, interference patterns are not always visible. Interference is a phenomena where two waves combine to create a new wave with a lower, higher, or identical amplitude. Optic or light interference is the type of interference that is most frequently observed. This is due to the fact that most sources produce light waves at random. This implies that the amplitude, frequency, and phase of the light waves emerging from a source are not constant.
• When the waves emitted from two sources have the same frequency and a fixed phase difference, they are said to be coherent.
• The randomly phased light waves constantly produce brilliant and dark fringes at every place, causing interference from such waves to occur all the time. However, because they happen at random, we cannot see them. One moment a point may have a dark fringe, the next it may have a dazzling fringe. As a result, the interference effect is neutralised and we simply perceive an average brightness value. Since we are unable to see the interference, it is not considered to be sustained.

Now, according to the given information, we are given that, two coherent light sources of intensities ratio 36:9 are employed in an interference experiment.

Then,

$\frac{I_{2} }{I_{1} } = \frac{36}{9}$

Now, we know that, the maximum intensity that is $I_{max}$ is equal to the square of the sum of the roots of the individual intensities.

Again, the minimum intensity that is $I_{min}$ is equal to the square of the difference of the roots of the individual intensities.

Now, ratio of the maximum intensity to the minimum intensity = $\frac{(1+\frac{6}{3}) ^{2} }{(1-\frac{6}{3}) ^{2} }$

Then, we get,

$\frac{I_{max} }{I_{min} } = \frac{9}{1} =9:1$.

Hence, the ratio of the intensities of the maxima and minima​ = 9:1.

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