Question

Two coherent light sources having intensity $I_1$ and $I_2$ . If the ratio of ${\displaystyle \frac{I_{Max}}{I_{Min}}}={\displaystyle \frac{16}{1}}$. Find ${\displaystyle \frac{I_1}{I_2}}=?$.

Answer 1

Hint: The ratio of intensities of first to second is equal to the square of ratio of their amplitudes. The ratio of maximum to minimum intensity is the square of sum of amplitudes to the difference of amplitudes. Thus by solving using this concept we will get the ratio of first intensity to the second intensity.

Formula used:
${\displaystyle \frac{I_{max}}{I_{min}}}={\left[{\displaystyle \frac{A_1+A_2}{A_1-A_2}}\right]}^2$
where, $A_{{}_{{}_1}}$and $A_2$ are the amplitude of coherent light source.
${\displaystyle \frac{I_1}{I_2}}={\left({\displaystyle \frac{A_1}{A_2}}\right)}^2$
$I_1$ and $I_2$ are the intensities of coherent light sources.

Complete step by step answer:
Given that,
${\displaystyle \frac{I_{max}}{I_{min}}}={\left[{\displaystyle \frac{A_1+A_2}{A_1-A_2}}\right]}^2$=${\displaystyle \frac{16}{1}}$
Taking the square root of the above equation we get,
${\displaystyle \frac{A_1+A_2}{A_1-A_2}}={\displaystyle \frac{4}{1}}$
$\Rightarrow$ $A_1+A_2=4(A_1-A_2)$
$\Rightarrow$ $5A_2=3A_1$
Then,
${\displaystyle \frac{A_1}{A_2}}={\displaystyle \frac{5}{3}}$
Therefore,
$\Rightarrow {\displaystyle \frac{I_1}{I_2}}={\left({\displaystyle \frac{A_1}{A_2}}\right)}^2$=${\left({\displaystyle \frac{5}{3}}\right)}^2={\displaystyle \frac{25}{9}}$

Thus the ratio of their intensity is ${\displaystyle \frac{25}{9}}$.

Additional information:
A coherent light may be a light that's capable of manufacturing radiation with waves vibrating in phase. The laser is an example of a coherent light . A laser produces coherent light through a process referred to as stimulated emission.
To set up a stable and clear interference pattern, two conditions must be met. The sources of the waves must be coherent. The waves should be monochromatic. That is, they should be of single wavelength or single colour.

Note:
The ratio of intensities of first to second is the ratio of square of their amplitudes. Note that the T ratio of intensities of first to second is not equal to the ratio of their amplitudes, but the square of their amplitudes.