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  • When one of the slits of Young's experiment is covered with a transparent sheet of thickness <img alt="\mathrm{4.8 \mathrm{~mm}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%

When one of the slits of Young's experiment is covered with a transparent sheet of thickness \mathrm{4.8 \mathrm{~mm}}, the central fringe shifts to a position originally occupied by the \mathrm{30^{\text {th }}} bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by \mathrm{20^{\text {th }}} bright fringe?

Option: 1

3.8 mm


Option: 2

1.6 mm


Option: 3

7.6 mm


Option: 4

3.2 mm


Answers (1)

best_answer

\mathrm{\begin{aligned} & \Delta \mathrm{x}=\frac{\mathrm{D}(\mu-1) \mathrm{t}}{\mathrm{d}} \text {. Also } \Delta \mathrm{x}=\frac{\mathrm{nD} \lambda}{\mathrm{d}} \\\\ & \therefore \quad \frac{\mathrm{D}(\mu-1) \mathrm{t}}{\mathrm{d}}=\frac{\mathrm{nD} \lambda}{\mathrm{d}} \text { or }(\mu-1) \mathrm{t}=\mathrm{n} \lambda \\\\ & \text { or } \quad \frac{\mathrm{t}_1}{\mathrm{t}_2}=\frac{\mathrm{n}_1}{\mathrm{n}_2} \Rightarrow \mathrm{t}_2=\frac{\mathrm{n}_2 \mathrm{t}_1}{\mathrm{n}_1} \\\\ & \text { or } \mathrm{t}_2=\frac{20 \times 4.8}{30}=3.2 \mathrm{~mm} \end{aligned}}

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Nehul

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