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In biprism experiment, if $5^{\text {th }}$ bright band with wavelength $\lambda_1^{\prime}$ coincides with $6^{\text {th }}$ dark band with wavelength $\lambda_2{ }^{\prime}$ then the ratio $\left(\frac{\lambda_2}{\lambda_1}\right)$ is
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Verified Answer
The correct answer is:
$\frac{10}{11}$
The fifth bright band will be:
$$
\mathrm{y}_5=\frac{5 \lambda_1 \mathrm{D}}{\mathrm{d}}
$$
$\therefore \quad$ The sixth dark band will be:
$$
\begin{aligned}
& \mathrm{y}_6{ }^{\prime}=\frac{11 \lambda_2 \mathrm{D}}{2 \mathrm{~d}} \\
& \text { Given: } \mathrm{y}_5=\mathrm{y}_6^{\prime} \\
\therefore \quad \frac{5 \lambda_1 \mathrm{D}}{\mathrm{d}} & =\frac{11 \lambda_2 \mathrm{D}}{2 \mathrm{~d}} \\
5 \lambda_1 & =\frac{11 \lambda_2}{2} \\
\frac{\lambda_2}{\lambda_1} & =\frac{10}{11}
\end{aligned}
$$
$$
\mathrm{y}_5=\frac{5 \lambda_1 \mathrm{D}}{\mathrm{d}}
$$
$\therefore \quad$ The sixth dark band will be:
$$
\begin{aligned}
& \mathrm{y}_6{ }^{\prime}=\frac{11 \lambda_2 \mathrm{D}}{2 \mathrm{~d}} \\
& \text { Given: } \mathrm{y}_5=\mathrm{y}_6^{\prime} \\
\therefore \quad \frac{5 \lambda_1 \mathrm{D}}{\mathrm{d}} & =\frac{11 \lambda_2 \mathrm{D}}{2 \mathrm{~d}} \\
5 \lambda_1 & =\frac{11 \lambda_2}{2} \\
\frac{\lambda_2}{\lambda_1} & =\frac{10}{11}
\end{aligned}
$$
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