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Q. No.In a standard double-slit experiment on interference, the vibrations emerging from the two slits are found to be in opposite phase. The fringe width is \(\delta.\) The first maximum on the screen occurs at a distance, from the centre, of:
| 1. | \(\Large\frac{\delta}{2}\) | 2. | \(\delta\) |
| 3. | \(\Large\frac{3\delta}{2}\) | 4. | zero |
Subtopic: Young's Double Slit Experiment |
Level 4: Below 35%
Hints
White light is used to illuminate the double slit in Young's double-slit experiment. Which of the following is/are true?
1. I only
2. I, II
3. I, III
4. I, II, III
| 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
Subtopic: Young's Double Slit Experiment |
Level 3: 35%-60%
Hints
Light of wavelength \(\lambda\) falls perpendicularly onto a single slit of width \(d\). A diffraction maximum is formed at \(P\) on a faraway screen placed parallel to plane of the slit. The first diffraction minimum is formed at \(Q,\) as shown on the screen. Let \(C\) be a 'point' so that it divides the slit \(AB\) in the ratio \(\dfrac{AC}{CB}=\dfrac12,\) i.e. \(AC\) represents the upper \(\dfrac13^{rd}\) of the slit. The total amplitude of the oscillation arriving from \(AC\) at \(Q\) is \(A_1\) and from \(CB\) at \(Q\) is \(A_2\).
Then:
1. \(2 A_{1}=A_{2}\)
2. \(A_{1}=2 A_{2}\)
3. \(\sqrt{2} A_{1}=A_{2}\)
4. \(A_{1}=A_{2}\)
Then:
1. \(2 A_{1}=A_{2}\)
2. \(A_{1}=2 A_{2}\)
3. \(\sqrt{2} A_{1}=A_{2}\)
4. \(A_{1}=A_{2}\)
Subtopic: Diffraction |
Level 3: 35%-60%
Hints
Plane waves of light of wavelength \(\lambda\) are incident onto a convex lens, and the beam is brought to a focus. A plane slab of thickness \(t\) having refractive indices \(\mu_1,~\mu_2\) in the upper and lower halves is placed parallel to the incoming wavefronts. The phase difference between the wavefronts at the focus, coming from the upper and lower halves of the slab is:
| 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. | \(\dfrac{2 \pi}{\lambda}\left(\dfrac{t}{\mu_{1}}+\dfrac{t}{\mu_{2}}\right)\) |
Subtopic: Huygens' Principle |
Level 3: 35%-60%
Hints
Young's double-slit experiment is conducted with light of an unknown wavelength, the waves arriving at the central point on the screen are found to have a phase difference of \(\dfrac{\pi}{2}.\) The closest maximum to the central point is formed behind one of the slits. The separation between the slits is \(d,\) and the slit to screen separation is \(D.\) The longest wavelength for this to happen is:
| 1. | \(\dfrac{2d^2}{D}\) | 2. | \(\dfrac{2d^2}{3D}\) |
| 3. | \(\dfrac{d^2}{2D}\) | 4. | \(\dfrac{d^2}{6D}\) |
Subtopic: Young's Double Slit Experiment |
Level 3: 35%-60%
Hints
Young's double-slit experiment is conducted with light of wavelength \(\lambda.\) The double-slit is shifted towards the source by a distance \(L,\) and the position of the \(5^{\text{th}}\) fringe is shifted by:
| 1. | \(\dfrac{5\lambda D}{d}\) | 2. | \(\dfrac{5\lambda L}{d}\) |
| 3. | \(\dfrac{5\lambda (L+D)}{d}\) | 4. | \(\dfrac{5\lambda (L-D)}{d}\) |
Subtopic: Young's Double Slit Experiment |
Level 3: 35%-60%
Hints
Sound waves travel faster in water than in air. Imagine a plane sound wavefront incident at an angle \(\alpha\) at the air-water interface; the refracted wavefront making an angle \(\beta\) with the interface. Then,
| 1. | \(\alpha>\beta\) |
| 2. | \(\beta>\alpha\) |
| 3. | \(\alpha=\beta\) |
| 4. | the relation between \(\alpha~\&~\beta \) cannot be predicted. |
Subtopic: Huygens' Principle |
Level 3: 35%-60%
Hints
Given below are two statements:
| Assertion (A): | Light waves of two different wavelengths, if allowed to superpose on a screen, will form an interference pattern but it will change with time. |
| Reason (R): | Light waves show interference and diffraction. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Interference vs Diffraction |
Level 3: 35%-60%
Hints
In a Young's double-slit experiment with identical slits (of slit separation-\(d,\) slit to screen distance \(D\)), the phase difference between the waves arriving at a point just opposite to one of the slits is \(\dfrac{\pi}{2}.\) The source is placed symmetrically with respect to the slits. The wavelength of light is:
| 1. | \(\dfrac{2d^2}{D}\) | 2. | \(\dfrac{d^2}{2D}\) |
| 3. | \(\dfrac{d^2}{D}\) | 4. | \(\dfrac{D^2}{d}\) |
Subtopic: Young's Double Slit Experiment |
53%
Level 3: 35%-60%
Hints
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. \(2.5\)
1. \(4\)
2. \(2\)
3. \(5\)
4. \(2.5\)
Subtopic: Young's Double Slit Experiment |
55%
Level 3: 35%-60%
Hints
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