A glass sphere of radius 12 cm has a small mark at a distance of 3 cm from its centre. Where will this mark appear when it is viewed from the side nearest to the mark along the line joining the centre and the mark?
1. | 8 cm inside the sphere | 2. | 12 cm inside the sphere |
3. | 4 cm inside the sphere | 4. | 3 cm inside the sphere |
A liquid of refractive index 1.33 is placed between two identical plano-convex lenses, with refractive index 1.50. Two possible arrangements, P and Q, are shown. The system is:
1. | divergent in P, convergent in Q | 2. | convergent in P, divergent in Q |
3. | convergent in both | 4. | divergent in both |
A ray of light falls on a prism ABC (AB=BC) and travels as shown in figure. The refractive index of the prism material should be greater than:
1. | \(4 /{3}\) | 2. | \( \sqrt{2}\) |
3. | \(1.5\) | 4. | \( \sqrt{3}\) |
Two similar plano-convex lenses are combined together in three different ways as shown in the adjoining figure. The ratio of the focal lengths in three cases will be:
1. 2 : 2 : 1
2. 1 : 1 : 1
3. 1 : 2 : 2
4. 2 : 1 : 1
On an optical bench a point object is placed at the mark of 10 cm, a convex lens of focal length 15 cm at the mark of 40 cm and a concave lens of focal length 15 cm placed at the mark of 60 cm. The final image is formed at the mark of: (point object and two lenses are coaxial)
1. 30 cm
2. 80 cm
3. 90 cm
4. infinity
Focal length of objective lens and eyepiece of an astronomical telescope are 200 cm and 10 cm respectively. The length of telescope for maximum magnification is nearly:
1. 207 cm
2. 210 cm
3. 204 cm
4. 220 cm
An object is placed at a point distance \(x\) from the focus of a convex lens and its image is formed at \(I\) as shown in the figure. The distances \(x\) and \(x'\) satisfy the relation:
1. \(\frac{x+x'}{2} = f\)
2. \(f = xx'\)
3. \(x+x' \le 2f\)
4. \(x+x' \ge 2f\)
A fish is a little away below the surface of a lake. If the critical angle is \(49^{\circ}\), then the fish could see things above the water surface within an angular range of \(\theta^{\circ}\) where:
1. \(\theta = 49^{\circ}\)
2. \(\theta = 90^{\circ}\)
3. \(\theta = 98^{\circ}\)
4. \(\theta = 24\frac{1}{2}^{\circ}\)
To increase the magnifying power of a telescope:
1. | The focal length of the eyepiece should be increased. |
2. | The focal length of the objective should be increased. |
3. | The wavelength of light should be increased. |
4. | The aperture of the eyepiece should be increased. |
The focal length of a glass lens in air is 20 cm. If it is dipped in water , its focal length in water will be:
1. | 80 cm | 2. | 40 cm |
3. | 60 cm | 4. | 20 cm |