A convex lens A of focal length \(20~\text{cm}\) and a concave lens \(B\) of focal length \(5~\text{cm}\) are kept along the same axis with the distance \(d\) between them. If a parallel beam of light falling on \(A\) leaves \(B\) as a parallel beam, then distance \(d\) in \(\text{cm}\) will be:
1. \(25\)
2. \(15\)
3. \(30\)
4. \(50\)
A ray of light is incident at an angle of incidence, \(i\), on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is \(\mu\), the angle of incidence \(i\), is nearly equal to:
1. \(\mu A\)
2. \(\dfrac{\mu A}{2}\)
3. \(\frac{A}{\mu}\)
4. \(\frac{A}{2\mu}\)
The refractive index of the material of a prism is 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. | \(30\) cm away from the mirror. |
2. | \(36\) cm away from the mirror. |
3. | \(30\) cm towards the mirror. |
4. | \(36\) 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. | \(\dfrac{y}{2x}\) |
A thin prism having refracting angle \(10^\circ\) is made of glass of a refractive index \(1.42\). This prism is combined with another thin prism of glass with a refractive index \(1.7\). This combination produces dispersion without deviation. The refracting angle of the second prism should be:
1. \(6^{\circ}\)
2. \(8^{\circ}\)
3. \(10^{\circ}\)
4. \(4^{\circ}\)
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 \(5\) cm deep when viewed from one surface and \(3\) cm deep when viewed from the opposite surface. The thickness (in 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. |