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Q. No.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 |
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A parallel beam of light of intensity \(I_0\) is incident on a lens and the intensity of the emerging beam is \(4I_0\) after it has traversed a further distance of \(30\) cm from the lens. The focal length of the lens is:
1. \(40\) cm
2. \(20\) cm
3. \(45\) cm
4. \(60\) cm
1. \(40\) cm
2. \(20\) cm
3. \(45\) cm
4. \(60\) cm
Subtopic: Â Lenses |
 51%
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A parallel beam is incident on to a lens of focal length \(f\) (positive), parallel to its principal axis. A thin prism of vertex angle \(A\) and refractive index \(\mu\) is inserted in the path of the parallel beam before it falls on the lens. The focal point of the image:
| 1. | remains unchanged |
| 2. | is displaced along \(+y\) by \((\mu-1)Af\) |
| 3. | is displaced along \(-y\) by \((\mu-1)Af\) |
| 4. | is displaced along \(+x\) by \((\mu-1)Af\) |
Subtopic: Â Prisms |
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Two convex lenses \((L_1,L_2)\) of focal lengths, \(20\) cm \((L_1)\) and \(40\) cm \((L_2),\) are placed co-axially at a separation of \(60\) cm. If a parallel beam of light is incident on \(L_1,\) the emerging beam from \(L_2\)
| 1. | is parallel but wider. | 2. | is parallel but narrower. |
| 3. | is convergent. | 4. | is divergent. |
Subtopic: Â Refraction at Curved Surface |
 56%
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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. | \(5\times 10^{-11}~\text{s}\) |
Subtopic: Â Refraction at Plane Surface |
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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 \(A.\)
Rays falling close to the highest point \((B)\) of the sphere are directed towards a point \(Q\) on the vertical diameter \(AB,\) after refraction. The distance \(BQ\) is:
Rays falling close to the highest point \((B)\) of the sphere are directed towards a point \(Q\) on the vertical diameter \(AB,\) after refraction. The distance \(BQ\) is:
| 1. | \(\dfrac{R}{2}\) | 2. | \(\dfrac{R\sqrt3}{\sqrt3 +1}\) |
| 3. | \(\dfrac{R\sqrt3}{2}\) | 4. | \(\dfrac{R\sqrt3}{\sqrt3 -1}\) |
Subtopic: Â Refraction at Curved Surface |
From NCERT
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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 |
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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 |
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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 |
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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 |
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