Q. No.Double-convex lenses are to be manufactured from a glass of refractive index \(1.55\) with both faces of the same radius of curvature. What is the radius of curvature required if the focal length is to be \(20~\text{cm}?\)
1. \(20~\text{cm}\)
2. \(22~\text{cm}\)
3. \(24~\text{cm}\)
4. \(15~\text{cm}\)
1. \(20~\text{cm}\)
2. \(22~\text{cm}\)
3. \(24~\text{cm}\)
4. \(15~\text{cm}\)
A small telescope has an objective lens of a focal length \(144~\text{cm}\) and an eyepiece of focal length \(6.0~\text{cm}.\) What is the magnifying power of the telescope?
| 1. | \(30\) | 2. | \(20\) |
| 3. | \(24\) | 4. | \(32\) |
A ray is incident at an angle of incidence \(i\) on one surface of a small angle prism (with the angle of the prism \(A\)) and emerges normally from the opposite surface. If the refractive index of the material of the prism is \(\mu,\) then the angle of incidence is nearly equal to:
| 1. | \(\dfrac{2A}{\mu}\) | 2. | \(\mu A\) |
| 3. | \(\dfrac{\mu A}{2}\) | 4. | \(\dfrac{A}{2\mu}\) |
A plane-convex lens of unknown material and unknown focal length is given. With the help of a spherometer, we can measure the
| 1. | focal length of the lens. |
| 2. | radius of curvature of the curved surface. |
| 3. | aperture of the lens. |
| 4. | refractive index of the material. |
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. | \(3f\) |
If the critical angle for total internal reflection from a medium to vacuum is \(45^{\circ}\), the velocity of light in the medium is:
| 1. | \(1.5\times10^{8}~\text{m/s}\) | 2. | \(\dfrac{3}{\sqrt{2}}\times10^{8}~\text{m/s}\) |
| 3. | \(\sqrt{2}\times10^{8}~\text{m/s}\) | 4. | \(3\times10^{8}~\text{m/s}\) |
For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index:
| 1. | lies between \(2\) and \(\sqrt{2}\) |
| 2. | is less than \(1\) |
| 3. | is greater than \(2\) |
| 4. | lies between \(\sqrt{2}\) and \(1\) |
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 student studying the similarities and differences between a camera and the human eye makes the following observations:
| (I) | both the eye and the camera have convex lenses. |
| (II) | in order to focus, the eye lens expands or contracts while the camera lens moves forward or backward. |
| (III) | the camera lens produces upside-down real images while the eye lens produces only upright real images. |
| (IV) | a screen in the camera is equivalent to the retina in the eyes. |
| (V) | a camera adjusts the amount of light entering it by adjusting the aperture of the lens. In the eye, the cornea controls the amount of light. |
The correct statements are:
| 1. | only (I), (II), (IV) |
| 2. | only (I), (III), (V) |
| 3. | only (I), (II), (IV), (V) |
| 4. | all of these |
A ray of white light is incident on a spherical water drop whose centre is \(\mathrm{C}\) as shown below. When observed from the opposite side, the emergent light:
| 1. | will be white and will emerge without deviating. |
| 2. | will be internally reflected. |
| 3. | will split into different colours such that the angles of deviation will be different for all colours. |
| 4. | will split into different colours such that the angles of deviation will be the same for all colours. |
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