In a Young's double slit experiment, 16 fringes are observed in a certain segment of the screen when light of wavelength $700 \mathrm{~nm}$ is used. If the wavelength of light is changed to 400 $\mathrm{nm}$, the number of fringes observed in the same segment of the screen would be :
Correct Option: , 4
(4) Let $n_{1}$ fringes are visible with light of wavelength $\lambda_{1}$ and $n_{2}$ with light of wavelength $\lambda_{2}$. Then
$\beta=\frac{n_{1} D \lambda_{1}}{d}=\frac{n_{2} D \lambda_{2}}{d}$ $\left(\because \beta=\frac{n \lambda D}{d}\right)$
$\Rightarrow \frac{n_{2}}{n_{1}}=\frac{\lambda_{1}}{\lambda_{2}} \Rightarrow n_{2}=\frac{700}{400} \times 16=28$
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