Question

in young's double slit experiment the slits are 0.2 mm apart and the screen is 1.5 m away it is observed that the distance between the central bright fringe and fourth dark fringe is 1.8 cm calculate the wavelength of the light used

Answer 1

Dear student,

$$\begin{gathered} \mathrm{Given},d=0.2\mathrm{mm} \\ D=1.5\mathrm{m} \\ n=4 \\ \mathrm{Distanc}\mathrm{between}\mathrm{the}\mathrm{central}\mathrm{bright}\mathrm{and}\mathrm{nth}\mathrm{dark}\mathrm{fring}=\left(n-\frac{1}{2}\right)\frac{D\lambda }{d} \\ \Rightarrow 1.8\times {10}^{-2}=\left(4-\frac{1}{2}\right)\times 1.5\times \frac{\lambda }{0.2\times {10}^{-3}} \\ \mathrm{On}\mathrm{solving}\mathrm{we}\mathrm{get}, \\ \lambda =6.85\times {10}^{-7}\mathrm{m} \end{gathered}$$
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