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. | \(\dfrac{y}{2x}\) |
1. \(45^\circ\)
2. \(30^\circ\)
3. \(55^\circ\)
4. \(50^\circ\)
An object is placed on the principal axis of a concave mirror at a distance of \(1.5f\) (\(f\) is the focal length). The image will be at:
| 1. | \(-3f\) | 2. | \(1.5f\) |
| 3. | \(-1.5f\) | 4. | \(3f\) |
(Where \(m\) is the magnification produced by the mirror)
| Column 1 | Column 2 | ||
| A. | \(m= -2\) | I. | convex mirror |
| B. | \(m= -\frac{1}{2}\) | II. | concave mirror |
| C. | \(m= +2\) | III. | real Image |
| D. | \(m= +\frac{1}{2}\) | IV. | virtual Image |
Codes:
| A | B | C | D | |
| 1. | I & III | I & IV | I & II | III & IV |
| 2. | I & IV | II & III | II & IV | II & III |
| 3. | III & IV | II & IV | II & III | I & IV |
| 4. | II & III | II & III | II & IV | I & IV |
| 1. | \(120^\circ\) | 2. | \(30^\circ\) |
| 3. | \(60^\circ\) | 4. | \(90^\circ\) |
A rod of length \(10~\text{cm}\) lies along the principal axis of a concave mirror of focal length \(10~\text{cm}\) in such a way that its end closer to the pole is \(20~\text{cm}\) away from the mirror. The length of the image is:
1. \(15~\text{cm}\)
2. \(2.5~\text{cm}\)
3. \(5~\text{cm}\)
4. \(10~\text{cm}\)
A beam of light is incident vertically on a glass slab of thickness \(1~\text{cm},\) and refractive index \(1.5.\) A fraction \(A\) is reflected from the front surface while another fraction \(B\) enters the slab and emerges after reflection from the back surface. The time delay between them is:
| 1. | \(10^{-10}~\text{s}\) | 2. | \(5\times 10^{-10}~\text{s}\) |
| 3. | \(10^{-11}~\text{s}\) | 4. | \(5\times 10^{-11}~\text{s}\) |
| 1. | \(\sin ^{-1}\left(\frac{10 t_1}{t_2}\right) \) | 2. | \(\sin ^{-1}\left(\frac{ t_2}{t_1}\right) \) |
| 3. | \(\sin ^{-1}\left(\frac{10 t_2}{t_1}\right) \) | 4. | \(\sin ^{-1}\left(\frac{ t_1}{10t_2}\right) \) |
| 1. | yellow, orange, and red |
| 2. | blue, green, and yellow |
| 3. | orange, red, and violet |
| 4. | all of the above |
| 1. | \(\text{tan}^{-1}(0.750)\) | 2. | \(\text{sin}^{-1}(0.500)\) |
| 3. | \(\text{sin}^{-1}(0.750)\) | 4. | \(\text{tan}^{-1}(0.500)\) |
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