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  • The ratio of the intensity at the centre of a bright fringe to the intensity at a point onequarter of the fringwidth from the centre isOption: 1 2</p

The ratio of the intensity at the centre of a bright fringe to the intensity at a point onequarter of the fringwidth from the centre is

Option: 1

2


Option: 2

1/2


Option: 3

4


Option: 4

16


Answers (1)

best_answer

Two waves of a single source having amplitude \mathrm{A} interfere. The resulting amplitude

\mathrm{A_{r}^{2}=A_{1}^{2}+A_{2}^{2}+2 A_{1} A \operatorname{Cos} \delta}

where \mathrm{A_{1}=A_{2}=A} and \mathrm{\delta=} phase difference between the waves
\mathrm{\Rightarrow \quad I_{r}=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \operatorname{Cos} \delta}

When the maxima occurs at the center, \mathrm{\delta=0}
\mathrm{\Rightarrow \quad \mathrm{r}_{\mathrm{r}_{1}}=4 \mathrm{I}\quad \ldots(1)}
Since the phase difference between two successive fringes is \mathrm{2 \pi},the phase difference between two points separated by a distance equal to one quarter of the distance between the two, successive fringes is equal to \mathrm{\delta=(2 \pi)\left(\frac{1}{4}\right)=\frac{\pi}{2}}. 

\mathrm{\Rightarrow \quad \mathrm{I}_{\mathrm{r}_{2}}=4 \mathrm{I} \cos ^{2}\left(\frac{\pi / 2}{2}\right)=2 \mathrm{l}\quad \ldots(2)}
Using (1) and (2)
\mathrm{\frac{\mathrm{I}_{\mathrm{r}_{1}}}{\mathrm{I}_{\mathrm{r}_{2}}}=\frac{4 \mathrm{I}}{2 \mathrm{I}}=2}

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vinayak

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