1. | \(\text{tan}^{-1}(0.750)\) | 2. | \(\text{sin}^{-1}(0.500)\) |
3. | \(\text{sin}^{-1}(0.750)\) | 4. | \(\text{tan}^{-1}(0.500)\) |
A concave lens with a focal length of \(-25~\text{cm}\) is sandwiched between two convex lenses, each with a focal length of \(40~\text{cm}.\) The power (in diopters) of the combined lens system would be:
1. | \(55\) | 2. | \(9\) |
3. | \(1\) | 4. | \(0.01\) |
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. | primary rainbow is due to double internal reflection and is formed above the secondary one. |
2. | primary rainbow is due to double internal reflection and is formed below the secondary one. |
3. | secondary rainbow is due to double internal reflection and is formed above the primary one. |
4. | secondary rainbow is due to a single internal reflection and is formed above the primary one. |
(a) | the distance between the objective and the eyepiece is \(20.02\text{m}.\) |
(b) | the magnification of the telescope is \(-1000\). |
(c) | the image of the planet is erect and diminished. |
(d) | the aperture of the eyepiece is smaller than that of the objective. |
1. | (a), (b), and (c) | 2. | (b), (c), and (d) |
3. | (c), (d), and (a) | 4. | (a), (b), and (d) |
1. | \(120^\circ\) | 2. | \(30^\circ\) |
3. | \(60^\circ\) | 4. | \(90^\circ\) |
1. | infinity | 2. | \(+2~\text{D}\) |
3. | \(+20 ~\text{D}\) | 4. | \(+5~\text{D}\) |
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. | \(-50~\text{cm}\) | 2. | \(40~\text{cm}\) |
3. | \(-40~\text{cm}\) | 4. | \(-100~\text{cm}\) |