# (a)  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. (b)  What kind of fringes do you expect to observe if white light is used instead of monochromatic light?

we know the intensity is directly proportional to the square of the amplitude
$I\alpha A^{2}$
Given that light intensity reduced to 50 %
Therefore

$\frac{I_{2}}{I_{1}}= 50 ^{0}/_{0}= \frac{1}{2}$

$\frac{I_{2}}{I_{1}}= \frac{A_{2}^{2}}{A_{1}^{2}}= \frac{1}{2}$
Therefore

$\frac{A_{2}}{A_{1}}= \frac{1}{\sqrt{2}}$
The ratio of maximum and minimum intensity is given as
$\frac{I_{maximum}}{I_{minimum}}= \left ( \frac{A_{1}+A_{2}}{A_{1}-A_{2}} \right )^2= \left ( \frac{1+\frac{A_{2}}{A_{1}}}{1-\frac{A_{2}}{A_{1}}} \right )^{2}$
$= \left ( \frac{1+\frac{1}{\sqrt{2}}}{1-\frac{1}{\sqrt{2}}} \right )^{2}=\left ( \frac{\sqrt{2}+1}{\sqrt{2}-1} \right )^2$
$\frac{I_{maximum}}{I_{minimum}}= 34$
b)
We know that the white light consists of different colours of different wavelength starting from violet to red. So when white light is used instead of monochromatic light separate interference pattern is formed for each wavelength the waves of all colours reach central fringe, so the central fringe remains white and the fringe on either side will be coloured. The violet colour near to the centre and red is far away from the centre. No clear fringe is seen after a few coloured fringes on either side of the central fringe.

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