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In a double slit experiment, $5^{\text {th }}$ dark fringe is formed opposite to one of the slits, the wavelength of light is
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Verified Answer
The correct answer is:
$\frac{\mathrm{d}^{2}}{9 \mathrm{D}}$
For dark fringe,
$$
\frac{x d}{D}=(2 m-1) \frac{\lambda}{2}
$$
Here, $m=5, x=\frac{d}{2}$
$\therefore \frac{d}{2} \cdot \frac{d}{D}=(2 \times 5-1) \frac{\lambda}{2}$
or $\frac{d^{2}}{D}=9 \lambda$
$\therefore$ Wavelength, $\lambda=\frac{d^{2}}{9 D}$
$$
\frac{x d}{D}=(2 m-1) \frac{\lambda}{2}
$$
Here, $m=5, x=\frac{d}{2}$
$\therefore \frac{d}{2} \cdot \frac{d}{D}=(2 \times 5-1) \frac{\lambda}{2}$
or $\frac{d^{2}}{D}=9 \lambda$
$\therefore$ Wavelength, $\lambda=\frac{d^{2}}{9 D}$
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