Answer to Question #102521 in Optics for ZZ

Question

Two coherent sources of light having intensity ratio 16:1 produce an interference fringe pattern. Calculate the ratio of the intensities of bright and dark fringes.

Answer 1

Let the intensities of individual source be $16 I\ \ \&\ I$

Bright fringe (maximum) intensity,

$\newline I_{max} = (\sqrt{I_1 } + \sqrt{I_2})^2$

Dark fringe (minimum) intensity,

$I _ {min} ​ =(\sqrt I _1 ​ ​ − \sqrt I _2 ​ ​ ) ^2$

$\dfrac {I_{ max}} { I _{ min} ​} ​ =\dfrac{ ( \sqrt I _ 1 + \sqrt I _ 2 ) ^ 2} { ( \sqrt I _1 - \sqrt I _ 2 ) ^ 2 } ​$

$\implies$ $\dfrac{I_{max}}{I_{min}}={\dfrac{(4+1)^2} {(4-1)^2}}=25:9$