Question 336: Wave Optics

Question

In Young's double slit experiment, the two slits are 'd' distance apart. Interference pattern is observed on a screen at a distance 'D' from the slits. A dark fringe is observed on a screen directly opposite to one of the slits. The wavelength of light is

Accepted Answer

$$\begin{aligned}
S_2 P & =\left(D^2+d^2ight)^{1 / 2} \
& =D\left[1+\frac{d^2}{D^2}ight]^{1 / 2}
\end{aligned}$$
Using binomial equation,
$$\mathrm{S}_2 \mathrm{P}=\mathrm{D}\left[1+\frac{1}{2} \frac{\mathrm{d}^2}{\mathrm{D}^2}ight]^{1 / 2}=\mathrm{D}+\frac{\mathrm{d}^2}{2 \mathrm{D}}$$
$$\Rightarrow$$ Path difference $$=\frac{d^2}{2 D}$$
For dark fringe, $$\frac{d^2}{2 D}=\frac{\lambda}{2}$$
$$	herefore \quad \lambda=\frac{d^2}{D}$$

Answer

$$\frac{\mathrm{D}^2}{2 \mathrm{~d}}$$

Answer

$$\frac{\mathrm{d}^2}{2 \mathrm{D}}$$

Answer

$$\frac{\mathrm{D}^2}{\mathrm{~d}}$$

Answer

$$\frac{d^2}{D}$$

Wave Optics

In Young's double slit experiment, the two slits are 'd' distance apart. Interference pattern is observed on a screen at a distance 'D' from the slits. A dark fringe is observed on a screen directly opposite to one of the slits. The wavelength of light is

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