Q105 / 125 · BITSAT 2017 · Physics

The ratio of intensity at the centre of a bright fringe to the intensity at a point distance one-fourth of the distance between two successive bright fringes will be

Solution

Intensity at centre of bright fringe,

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

$I_{0} = 2 I + 2 I$ $[∵ \cos 0 ° = 1]$

$= 4 I$

Similarly Intensity at point $\frac{P}{4}$

(with phase difference $= \frac{2 π}{4} = \frac{π}{2}$ )

$I^{'} = I + I + 2 \sqrt{I I} \cos \frac{π}{2}$

$= 2 I + 2 \sqrt{I I} \times 0$

$= 2 I$

$∴ \frac{I_{0}}{I^{'}} = \frac{4 I}{2 I} = 2$

Hence, the correct answer is option: 'C'.