Two coherent sources have intensities in the ratio $25 : 16$ . Find the ratio of intensities of maxima to minima?

Open in App

Solution

Now,
$\frac{I_{1}}{I_{2}} = \frac{{a_{1}}^{2}}{{a_{2}}^{2}} (\frac{I_{1}}{I_{2}} = \frac{25}{16})$
$\Rightarrow \frac{{a_{1}}^{2}}{{a_{2}}^{2}} = \frac{25}{16}$
$\frac{a_{1}}{a_{2}} = \frac{5}{4}$
Now, $\frac{I_{m a x}}{I_{m i n}} = (\frac{a_{1} + a_{2}}{a_{1} + a_{2}})^{2} = (\frac{5 + 4}{5 - 4})^{2} = (\frac{9}{1})^{2}$
$\Rightarrow \frac{I_{m a x}}{I_{m i n}} = \frac{81}{1}$
Thus, the ratio of intensity of maximum to minimum is $81 : 1$

Suggest Corrections

Similar questions

Q. Two coherent sources of intensity ratio

9 : 4

produce interference. The intensity ratio of maxima and minima of the interference pattern is:

Two coherent sources of intensity ratio 100:1 interfere. The ratio of interference at the maxima and minima

Q. Two coherent light sources whose intensity ratio is

81 : 1

produce interference fringes. If the ratio of intensities of maxima and minima in the fringe system is x:y. Find x-y?

Two coherent light sources of intensity ratio n are employed in an inteference experiment. The ratio of the intensities of the maxima and minima in the inteference pattern is

Q. Two coherent sources of different intensities sound waves interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio:

Join BYJU'S Learning Program

Two coherent sources have intensities in the ratio 25:16. Find the ratio of intensities of maxima to minima?

Now,I1I2=a12a22(I1I2=2516)⇒a12a22=2516a1a2=54Now, ImaxImin=(a1+a2a1+a2)2=(5+45−4)2=(91)2⇒ImaxImin=811Thus, the ratio of intensity of maximum to minimum is 81:1

Two coherent sources have intensities in the ratio $25 : 16$ . Find the ratio of intensities of maxima to minima?