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Q. No.An equi-convex lens of focal length \(20\) cm (in the air) is split into two parts by a surface that has half the curvature of either of its outer surfaces. The ratio of the powers of the two lenses thus formed is:
1. \(3:1\)
2. \(2:1\)
3. \(1:1\)
4. \(-2:1\)
Subtopic: Â Lenses |
Level 4: Below 35%
Hints
An equi-convex lens of focal length \(50~\text{cm}\) and an equi-concave lens of the same focal length are placed \(50~\text{cm}\) apart, with a common principal axis. A point object is placed on the principal axis of the system, at a distance of \(100~\text{cm}\) in front of the convex lens (see figure). The final image is formed at:
| 1. | \(100~\text{cm}\) in front of the concave lens |
| 2. | \(50~\text{cm}\) in front of the concave lens |
| 3. | \(50~\text{cm}\) behind the concave lens |
| 4. | infinity |
Subtopic: Â Lenses |
 58%
Level 3: 35%-60%
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A plano-convex lens made of glass \((\mu=1.5)\) is placed with its convex surface in a liquid, and it is found that the focal length is doubled. The refractive index of the liquid is:
1. \(3\)
2. \(2\)
3. \(1.25\)
4. \(1.2\)
1. \(3\)
2. \(2\)
3. \(1.25\)
4. \(1.2\)
Subtopic: Â Lenses |
Level 3: 35%-60%
Hints
An equiconvex lens of focal length \(100\) cm is split into two plano-convex lenses and the plane surface of one of these lenses is silvered. This acts as a:
| 1. | converging mirror of focal length \(200\) cm. |
| 2. | converging mirror of focal length \(100\) cm. |
| 3. | diverging mirror of focal length \(200\) cm. |
| 4. | diverging mirror of focal length \(100\) cm. |
Subtopic: Â Lenses |
Level 3: 35%-60%
Hints
Two identical equilateral triangular prisms, each of which gives a minimum deviation of \(60^{\circ}\) are taken: call these prisms \(A,B\). These are placed as shown in the figure, and a ray of light is incident on prism \(A\) at minimum deviation. Now prism \(B\) is cut in half, along the dotted line, and the right half is removed. The deviation of the emerging ray is:
| 1. | \(90^{\circ}\) | 2. | \(45^{\circ}\) |
| 3. | \(60^{\circ}\) | 4. | \(30^{\circ}\) |
Subtopic: Â Prisms |
 50%
Level 3: 35%-60%
Hints
A convex lens of focal length \(60\) cm is placed in the path of a parallel beam, falling parallel to its principal axis. A plane mirror is placed on the principal axis, making an angle of \(45^{\circ}\) with it, at a distance of \(30\) cm behind the lens. The distance of the new focus from lens (optical centre) is:
1. \(60\) cm
2. \((60+30\sqrt2)\) cm
3. \(60\sqrt2\) cm
4. \(30\sqrt2\) cm
1. \(60\) cm
2. \((60+30\sqrt2)\) cm
3. \(60\sqrt2\) cm
4. \(30\sqrt2\) cm
Subtopic: Â Lenses |
Level 3: 35%-60%
Hints
An empty cylindrical beaker whose height is equal to its diameter is kept on a table. An observer's eye\((E)\) looking towards \(S\) (line of sight: \(ES\)) can see the point \(Q\) on the lower right. The angle of view, \(\theta,\) is the angle the line of sight \(ES,\) makes with the vertical \(RS\)-extended. A transparent liquid is now slowly poured into the beaker. As the liquid level rises in the beaker, the line of sight has to be continually adjusted (by increasing angle \(\theta\)) in order to keep \(Q\) visible. When the liquid fills the beaker to the brim, \(Q\) can no more be seen by adjusting the line of sight \(ES. \) The minimum refractive index of the liquid should be:
| 1. | \(\dfrac32\) | 2. | \(2\) |
| 3. | \(\sqrt{\dfrac32} \) | 4. | \(\sqrt2\) |
Subtopic: Â Total Internal Reflection |
Level 3: 35%-60%
Hints
Assume that the corner of \(O\) of the room is the origin, and the axes \(x,y,z\) are along the edges. The three walls meeting orthogonally at \(O\) are perfect mirrors. A ray of light travelling parallel to the vector \(-(\hat i+2\hat j+\hat k)\) is incident on the \(y\text-z\) mirror (wall). The emerging ray, after all reflections, will be along:
| 1. | \(\hat i-2\hat j-\hat k\) |
| 2. | \(\hat i+\hat k-2\hat j\) |
| 3. | \(-\hat i+2\hat j+\hat k\) |
| 4. | \(\hat i+2\hat j+\hat k\) |
Subtopic: Â Reflection at Plane Surface |
Level 3: 35%-60%
Hints
An equilateral triangular prism of glass \((\mu=1.5)\) is placed in air. A ray of light is incident normally onto the surface \(AB.\) The ray will finally emerge:
| 1. | normally from the surface \(BC.\) |
| 2. | normally from the surface \(AC.\) |
| 3. | either from the surface \(BC\) or \(AC,\) normally. |
| 4. | either from the surface \(BC\) or \(AC,\) at an angle of emergence greater than \(60^{\circ}\) but less than \(90^{\circ}.\) |
Subtopic: Â Total Internal Reflection |
Level 4: Below 35%
Hints
A solid sphere (centre \(O\)) of homogeneous transparent material kept upright has rays parallel to its vertical diameter falling on it. A ray that is aimed at \(P,\) where the horizontal distance \(OP=\dfrac{\sqrt3}{2}R\) (\(R\) being the sphere's radius), undergoes refraction at the sphere's surface and strikes the lowest point \(A.\)
The refractive index of the material of the sphere is:
1. \(2\)
2. \(\sqrt2\)
3. \(\sqrt3\)
4. \(\sqrt{\dfrac32} \)
The refractive index of the material of the sphere is:
1. \(2\)
2. \(\sqrt2\)
3. \(\sqrt3\)
4. \(\sqrt{\dfrac32} \)
Subtopic: Â Refraction at Curved Surface |
 50%
Level 3: 35%-60%
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