1. If one of two identical slits producing interference in Young’… - Vidyadip

Question

If one of two identical slits producing interference in Young’s experiment is covered with glass, so that the light intensity passing through it is reduced to 50%, find the ratio of the maximum and minimum intensity of the fringe in the interference pattern.
What kind of fringes do you expect to observe if white light is used instead of monochromatic light?

✓

Answer

$\text{I}_1=\frac{\text{I}}{2}$

$\text{I}_2=\text{I}$

$\frac{\text{I}_{\text{max}}}{\text{I}_{\text{min}}}=\bigg(\frac{\sqrt{\text{I}_1}+\sqrt{\text{I}_2}}{\sqrt{\text{I}_1}-\sqrt{\text{I}_2}}\bigg)^2$

$=\Bigg(\frac{\sqrt{\frac{\text{I}}{2}}+\sqrt{\text{I}}}{\sqrt{\frac{\text{I}}{2}}-\sqrt{\text{I}}}\Bigg)^2$

$=\bigg(\frac{1+\sqrt{2}}{1-\sqrt{2}}\bigg)^2$

$=\frac{2+1+2\sqrt{2}}{2+1-2\sqrt{2}}$

$=\frac{3+2\sqrt{2}}{3-2\sqrt{2}}$

If we use white light, central fringe will be white, then there will be colourful fringes on both sides, starting from violet to red (fringe width $\propto$ wavelength) and then there will be general illumination of screen.

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