Question

Two slits in Young's experiment have widths in the ratio 81 : 1. What is the ratio of the amplitudes of light waves coming from them?

Answer 1

Given,
Let w₁ and w₂ be the width of two slits.
$\frac{{\mathrm{w}}_1}{{\mathrm{w}}_2}=\frac{81}{1}$
Let I₁ and I₂ be the intensity of light wave and a₁ and a₂ be the amplitudes of the light waves. then,
$\frac{{\mathrm{w}}_1}{{\mathrm{w}}_2}=\frac{{\mathrm{I}}_1}{{\mathrm{I}}_2}=\frac{{\mathrm{a}}_1^2}{{\mathrm{a}}_2^2}$
$\Rightarrow \frac{81}{1}=\frac{{\mathrm{a}}_1^2}{{\mathrm{a}}_2^2}$
$\Rightarrow \frac{9}{1}=\frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}$