Q. No.The refractive index of the material of a prism is \(\sqrt{2}\) and the angle of the prism is \(30^\circ.\) One of the two refracting surfaces of the prism is made a mirror inwards with a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is:
1.
\(60^\circ\)
2.
\(45^\circ\)
3.
\(30^\circ\)
4.
zero
| 1. | \(30~\text{cm}\) away from the mirror. |
| 2. | \(36~\text{cm}\) away from the mirror. |
| 3. | \(30~\text{cm}\) towards the mirror. |
| 4. | \(36~\text{cm}\) towards the mirror. |
A beam of light from a source \(L\) is incident normally on a plane mirror fixed at a certain distance \(x\) from the source. The beam is reflected back as a spot on a scale placed just above the source \(L.\) When the mirror is rotated through a small angle \(\theta,\) the spot of the light is found to move through a distance \(y\) on the scale. The angle \(\theta\) is given by:
| 1. | \(\dfrac{y}{x}\) | 2. | \(\dfrac{x}{2y}\) |
| 3. | \(\dfrac{x}{y}\) | 4. | \(\dfrac{y}{2x}\) |
Two identical glass \(\left(\mu_g = \frac{3}{2}\right )\) equiconvex lenses of focal length \(f\) each are kept in contact. The space between the two lenses is filled with water \(\left(\mu_w = \frac{4}{3}\right)\). The focal length of the combination is:
| 1. | \(\dfrac{f}{3}\) | 2. | \(f\) |
| 3. | \(\dfrac{4f}{3}\) | 4. | \(\dfrac{3f}{4}\) |
An air bubble in a glass slab with a refractive index \(1.5\) (near-normal incidence) is \(5~\text{cm}\) deep when viewed from one surface and \(3~\text{cm}\) deep when viewed from the opposite surface. The thickness (in \(\text{cm}\)) of the slab is:
| 1. | \(8\) | 2. | \(10\) |
| 3. | \(12\) | 4. | \(16\) |
A person can see objects clearly only when they lie between \(50\) cm and \(400\) cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be:
| 1. | convex, \(+2.25\) D | 2. | concave, \(-0.25\) D |
| 3. | concave, \(-0.2\) D | 4. | convex, \(+0.5\) D |
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. |
| 1. | \(46.0\text{cm}\) | 2. | \(50.0\text{cm}\) |
| 3. | \(54.0\text{cm}\) | 4. | \(37.3\text{cm}\) |
| 1. | \(45^{0},~\sqrt{2}\) | 2. | \(30^{0},~\sqrt{2}\) |
| 3. | \(30^{0},~\frac{1}{\sqrt{2}}\) | 4. | \(45^{0},~\frac{1}{\sqrt{2}}\) |
In an astronomical telescope in normal adjustment, a straight line of length \(L\) is drawn on the inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is \(l.\) The magnification of the telescope is:
1. \(\frac{L}{l}+1\)
2. \(\frac{L}{l}-1\)
3. \(\frac{L+1}{l-1}\)
4. \(\frac{L}{l}\)
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