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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. \(2.5\)
Subtopic: Young's Double Slit Experiment |
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The width of the central maximum of the diffraction pattern of a single slit of width \(1\) mm equals the width of the slit itself, when the screen is \(1\) m away from it. The wavelength of light used equals:
| 1. | \(250\) nm | 2. | \(500\) nm |
| 3. | \(1000\) nm | 4. | \(2000\) nm |
Subtopic: Diffraction |
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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. \(\dfrac{2 \pi}{\lambda}\left(\dfrac{t}{\mu_{1}}+\dfrac{t}{\mu_{2}}\right)\)
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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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 \(\frac{AC}{CB}=\frac12,\) i.e. \(AC\) represents the upper \(\frac13^{rd}\) 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 |
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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. |
1. I only
2. I, II
3. I, III
4. I, II, III
Subtopic: Young's Double Slit Experiment |
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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 \(\frac{\pi}{2}.\) 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. \(\frac{2d^2}{D}\)
2. \(\frac{2d^2}{3D}\)
3. \(\frac{d^2}{2D}\)
4. \(\frac{d^2}{6D}\)
1. \(\frac{2d^2}{D}\)
2. \(\frac{2d^2}{3D}\)
3. \(\frac{d^2}{2D}\)
4. \(\frac{d^2}{6D}\)
Subtopic: Young's Double Slit Experiment |
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A linearly polarized monochromatic light of intensity \(10\) lumen is incident on a polarizer. The angle between the direction of polarization of the light and that of the polarizer such that the intensity of output light is \(2.5\) lumen is:
| 1. | \(60^\circ\) | 2. | \(75^\circ\) |
| 3. | \(30^\circ\) | 4. | \(45^\circ\) |
Subtopic: Polarization of Light |
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A monochromatic light of frequency \(500\) THz is incident on the slits of a Young's double slit experiment. If the distance between the slits is \(0.2\) mm and the screen is placed at a distance \(1\) m from the slits, the width of \(10\) fringes will be:
1. \(1.5\) mm
2. \(15\) mm
3. \(30\) mm
4. \(3\) mm
Subtopic: Young's Double Slit Experiment |
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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 |
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