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In biprism experiment, 21 fringes are observed in a given region using light of wavelength $480 Å$. If light of wavelength $560 Å$ is used, the number of fringes in the same region will be
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The correct answer is:
18
$$
\mathrm{n}_1 \beta_1=\mathrm{n}_2 \beta_2
$$
$$
21 \times \frac{\lambda_1 \mathrm{D}}{\mathrm{d}}=\mathrm{n}_2 \times \frac{\lambda_2 \mathrm{D}}{\mathrm{d}}
$$
$$
\mathrm{n}_2=21 \times \frac{\lambda_1}{\lambda_2}=\frac{21 \times 480}{560}=18
$$
\mathrm{n}_1 \beta_1=\mathrm{n}_2 \beta_2
$$
$$
21 \times \frac{\lambda_1 \mathrm{D}}{\mathrm{d}}=\mathrm{n}_2 \times \frac{\lambda_2 \mathrm{D}}{\mathrm{d}}
$$
$$
\mathrm{n}_2=21 \times \frac{\lambda_1}{\lambda_2}=\frac{21 \times 480}{560}=18
$$
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