Q. No.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. \(\frac{L}{l}\)
The prism will:
| 1. | separate the blue colour part from the red and green colour. |
| 2. | separate all three colours from one another. |
| 3. | not separate the three colours at all. |
| 4. | separate the red colour part from the green and blue colours. |
Two identical thin plano-convex glass lenses (refractive index = \(1.5\)) each having radius of curvature of \(20\) cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of a refractive index of \(1.7\). The focal length of the combination is:
1. \(-20\) cm
2. \(-25\) cm
3. \(-50\) cm
4. \(50\) cm
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