The ratio of intensity at the centre of a bright fringe to the...

Intensity at centre of bright fringe,

${I}_{0} = I + I + 2\sqrt{II} \cdot \cos 0$

${I}_{0} = 2I + 2I$~ \left[∵ \cos 0 ° = 1\right]$</p><p>$= 4I$</p><p>Similarly Intensity at point$\dfrac{P}{4}$</p><p>(with phase difference$= \dfrac{2\pi}{4} = \dfrac{π}{2}$)</p><p>$I^{'} = I + I + 2\sqrt{II}cos\dfrac{π}{2}$</p><p>$= 2I + 2\sqrt{II} \times 0$</p><p>$= 2I$</p><p>$∴ \dfrac{I0}{I '} = \dfrac{4I}{2I} = 2