Question 98: Wave Optics

Question

In a Young's double slit experiment, two slits are illuminated with a light of wavelength $$800 \mathrm{~nm}$$. The line joining $$A_{1} P$$ is perpendicular to $$A_{1} A_{2}$$ as shown in the figure. If the first minimum is detected at $$P$$, the value of slits separation 'a' will be:
The distance of screen from slits D = 5 cm

Accepted Answer

$A_{2} P-A_{1} P=\frac{\lambda}{2} \quad$ (Condition of minima)
$$
\sqrt{\mathrm{D}^{2}+\mathrm{a}^{2}}-\mathrm{D}=\frac{\lambda}{2}
$$
$$
\begin{aligned}
& \mathrm{D}\left(1+\frac{\mathrm{a}^{2}}{\mathrm{D}^{2}}ight)^{1 / 2}-\mathrm{D}=\frac{\lambda}{2} \\
& \mathrm{D}\left(1+\frac{1}{2} 	imes \frac{\mathrm{a}^{2}}{\mathrm{D}^{2}}ight)-\mathrm{D}=\frac{\lambda}{2} \\
& \frac{\mathrm{a}^{2}}{2 \mathrm{D}}=\frac{\lambda}{2} \Rightarrow \mathrm{a}=\sqrt{\lambda \cdot \mathrm{D}} \\
& =\sqrt{800 	imes 10^{-6} 	imes 50}
\end{aligned}
$$
$\mathrm{a}=0.2 \mathrm{~mm}$

Answer

0.2 mm

Answer

0.5 mm

Answer

0.4 mm

Answer

0.1 mm

Wave Optics

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