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Q. No.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. \(A_{1}=A_{2}\)
Subtopic: Diffraction |
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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 |
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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 |
51%
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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 |
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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 |
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Young's double-slit experiment is performed with identical slits separated by a distance \(d,\) and with light of wavelength \(\lambda.\) The screen is placed at a point which is at a distance \(D\) from the double-slit, as usual. A convex lens of focal length \(f\) is inserted between the double-slit and the screen, very close to the double slit. The screen is adjusted (i.e. the value of \(D\) is slowly varied) until a clear interference pattern is formed. The fringe width equals:
| 1. | \(\dfrac{\lambda f}{d}\) | 2. | \(\dfrac{2\lambda f}{d}\) |
| 3. | \(\dfrac{\lambda f}{2d}\) | 4. | \(\dfrac{\lambda f}{d\sqrt2}\) |
Subtopic: Young's Double Slit Experiment |
58%
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Electrons (mass \(m\)) moving with a velocity \(v\) are incident normally onto a single slit of width \(d,\) and are detected on a screen placed at a distance \(D\) behind the slit. The central point on the screen where most of the electrons are detected is \(O.\) The closest point to \(O\) where no electrons are detected is \(X.\) Then \(OX\) equals:
| 1. | \(\dfrac{hD}{mvd}\) | 2. | \(\dfrac{hD}{2mvd}\) |
| 3. | \(\dfrac{2hD}{mvd}\) | 4. | \(\dfrac{3hD}{2mvd}\) |
Subtopic: Diffraction |
62%
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In a Young's double-slit experimental setup, \(240\) fringes are observed to be formed in a region of the screen when light of wavelength \(450\) nm is used. If the wavelength of light is changed to \(600\) nm, the number of fringes formed in the same region will be:
| 1. | \(135\) | 2. | \(180\) |
| 3. | \(320\) | 4. | \(428\) |
Subtopic: Young's Double Slit Experiment |
73%
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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 |
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Young's double-slit experiment is conducted with the light of wavelength, \(\lambda=4500~\mathring A\) and \(400\) fringes are observed in a \(10\) cm region on the screen. The apparatus is immersed in a clear liquid of refractive index \(\mu=2.\) The number of fringes observed will be:
1. \(400\)
2. \(800\)
3. \(200\)
4. \(1600\)
1. \(400\)
2. \(800\)
3. \(200\)
4. \(1600\)
Subtopic: Young's Double Slit Experiment |
63%
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