Q. No.Find the minimum order of a green fringe (\(\lambda = 500\) nm) which overlaps a dark fringe of violet (\(\lambda = 400\) nm) in a Young's double-slit experiment conducted with these two colours.
1. \(4\)
2. \(2\)
3. \(5\)
4. \(2.5\)
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| 1. | \(\dfrac{5}{3}\) | 2. | \(\dfrac{3}{1}\) |
| 3. | \(\dfrac{25}{9}\) | 4. | \(\dfrac{9}{1}\) |
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| 1. | \(10~\mu \text{m}\) | 2. | \(1~\mu \text{m}\) |
| 3. | \(17~\mu \text{m}\) | 4. | \(1.7~\mu \text{m}\) |
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| 1. | \(250\) nm | 2. | \(500\) nm |
| 3. | \(1000\) nm | 4. | \(2000\) nm |
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| 1. | \(\dfrac{2 \pi}{\lambda}\left[\left(\mu_{1}-1\right) t+\left(\mu_{2}-1\right) t\right]\) |
| 2. | \(\dfrac{2 \pi}{\lambda}\left(\mu_{1}-\mu_{2}\right) t\) |
| 3. | \(\dfrac{2 \pi}{\lambda}\left(\dfrac{t}{\mu_{1}}-\dfrac{t}{\mu_{2}}\right)\) |
| 4. | \(\dfrac{2 \pi}{\lambda}\left(\dfrac{t}{\mu_{1}}+\dfrac{t}{\mu_{2}}\right)\) |
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Then:
1. \(2 A_{1}=A_{2}\)
2. \(A_{1}=2 A_{2}\)
3. \(\sqrt{2} A_{1}=A_{2}\)
4. \(A_{1}=A_{2}\)
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| I. | The central fringe will be white. |
| II. | Closest bright fringe to the central fringe will be a violet fringe. |
| III. | There will not be any dark fringe. |
2. I, II
3. I, III
4. I, II, III
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1. \(125~\text{nm}\)
2. \(250~\text{nm}\)
3. \(500~\text{nm}\)
4. \(1000~\text{nm}\)
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| 1. | \(\dfrac{5\lambda D}{d}\) | 2. | \(\dfrac{5\lambda L}{d}\) |
| 3. | \(\dfrac{5\lambda (L+D)}{d}\) | 4. | \(\dfrac{5\lambda (L-D)}{d}\) |
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| 1. | \(\dfrac{2d^2}{D}\) | 2. | \(\dfrac{d^2}{2D}\) |
| 3. | \(\dfrac{d^2}{D}\) | 4. | \(\dfrac{D^2}{d}\) |
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