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Q. No.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
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. \(-2:1\)
1. \(3:1\)
2. \(2:1\)
3. \(1:1\)
4. \(-2:1\)
Subtopic: Â Lenses |
Level 4: Below 35%
Hints
Given below are two statements:
| Assertion (A): | If two converging lenses are introduced into the path of a parallel beam of light, the emerging beam cannot be diverging. |
| Reason (R): | The converging lenses have positive powers. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Â Lenses |
Level 4: Below 35%
Hints
Given below are two statements:
| Assertion (A): | Parallel rays of light of different colours fail to converge to a point after reflection from a spherical mirror. |
| Reason (R): | The refractive index of any material depends on the frequency of light. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is a correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not a correct explanation of (A). |
Subtopic: Â Reflection at Spherical Surface |
Level 4: Below 35%
Hints
The following diagram shows light travelling from \(A\) to \(B\) after bouncing off a plane mirror at \(P\). The time taken is \(t_{APB}\). If, however, light were to take a different path, \(AQB\) (shown by the dotted line), the time taken is \(t_{AQB}\).
Then,
Then,
| 1. | \(t_{APB}=t_{AQB}\) |
| 2. | \(t_{APB}<t_{AQB}\) |
| 3. | \(t_{APB}>t_{AQB}\) |
| 4. | \(t_{APB}\) maybe greater than or less than \(t_{AQB}\) depending on whether \(Q\) is to the left or right of \(P\). |
Subtopic: Â Reflection at Plane Surface |
Level 4: Below 35%
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
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 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
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
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%
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