Q. No.The ratio of resolving powers of an optical microscope for two wavelengths =4000 and is:-
1. 9:4
2. 3:2
3. 16:81
4. 8:27
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| 1. | \(\dfrac{I_0}{4}\) | 2. | \(\dfrac{I_0}{8}\) |
| 3. | \(\dfrac{I_0}{16}\) | 4. | \(\dfrac{I_0}{2}\) |
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The interference pattern is obtained with two coherent light sources of intensity ratio n. In the interference pattern, the ratio will be
1.
2.
3.
4.
A linear aperture whose width is \(0.02\) cm is placed immediately in front of a lens of focal length \(60\) cm. The aperture is illuminated normally by a parallel beam of wavelength \(5\times 10^{-5}\) cm. The distance of the first dark band of the diffraction pattern from the center of the screen is:
1. \(0.10~\text{cm}\)
2. \(0.25~\text{cm}\)
3. \(0.20~\text{cm}\)
4. \(0.15~\text{cm}\)
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In Young's double-slit experiment, the separation \(d\) between the slits is \(2\) mm, the wavelength \(\lambda\) of the light used is \(5896~\mathring{A}\) and distance \(D\) between the screen and slits is \(100\) cm. It is found that the angular width of the fringes is \(0.20^{\circ}\). To increase the fringe angular width to \(0.21^{\circ}\) (with same \(\lambda\) and \(D\)) the separation between the slits needs to be changed to:
1. \(1.8\) mm
2. \(1.9\) mm
3. \(2.1\) mm
4. \(1.7\) mm
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An astronomical refracting telescope will have large angular magnification and high angular resolution when it has an objective lens of:
| 1. | Small focal length and large diameter |
| 2. | Large focal length and small diameter |
| 3. | Large focal length and large diameter |
| 4. | Small focal length and small diameter |
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The intensity at the maximum in a Young's double-slit experiment is \(I_0\). Distance between two slits is \(d = 5\lambda,\) where \(\lambda\) is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance \(D = 10d\)?
1. \(\frac{I_0}{4}\)
2. \(\frac{3I_0}{4}\)
3. \(\frac{I_0}{2}\)
4. \(I_0\)
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Two slits in young’s experiment have widths in the ratio 1:25. The ratio of intensity at the maxima and minima in the interference pattern is
1.
2.
3.
4.
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1. \(\frac{\pi}{4}~\text{radian}\)
2. \(\frac{\pi}{2}~\text{radian}\)
3. \(\pi~\text{radian}\)
4. \(\frac{\pi}{8}~\text{radian}\)
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