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A parallel beam of width \(20\) mm is incident onto a lens and the width of the emerging beam decreases at a rate of \(1\) mm as it travels every \(3\) cm. The lens has a focal length of:
1.
\(30\) cm
2.
\(60\) cm
3.
\(\dfrac{20}3\) cm
4.
\(\dfrac{40}{3}\) cm
Subtopic: Lenses |
63%
Level 2: 60%+
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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: 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. \(\hat i+2\hat j+\hat k\)
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: 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: Total Internal Reflection |
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: Lenses |
Level 4: Below 35%
Hints
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: Lenses |
52%
Level 3: 35%-60%
Hints
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: Prisms |
Level 3: 35%-60%
Hints
A point object \((A)\) is placed on the principal axis of a convex lens (focal length = \(30~\text{cm}\)) at a distance of \(45~\text{cm}\) from it. The image is formed at position \(B.\) If the object \(A\) is moved up by \(1~\text{cm}\) then the image moves:
1. down by \(1~\text{cm}\)
2. down by \(2~\text{cm}\)
3. up by \(1~\text{cm}\)
4. up by \(2~\text{cm}\)
1. down by \(1~\text{cm}\)
2. down by \(2~\text{cm}\)
3. up by \(1~\text{cm}\)
4. up by \(2~\text{cm}\)
Subtopic: Lenses |
65%
Level 2: 60%+
Hints
An incident ray falling at an angle of \(30^\circ\) with the \(x\)-axis is reflected by a mirror to a (reflected) ray making \(60^\circ\) with the \(x\)-axis. The angle made by the mirror's surface (not shown in the diagram) with the \(x\)-axis is:
1. \(15^\circ\)
2. \(45^\circ\)
3. \(75^\circ\)
4. \(105^\circ\)
1. \(15^\circ\)
2. \(45^\circ\)
3. \(75^\circ\)
4. \(105^\circ\)
Subtopic: Reflection at Plane Surface |
64%
Level 2: 60%+
Hints
A ray of light falling on a \(2^\circ\)-prism (thin prism) undergoes a \(3^\circ\)-deviation on the first surface and no deviation on the second. The refractive index of the material of the prism is:
1. \(1.5\)
2. \(1.75\)
3. \(2.0\)
4. \(2.5\)
1. \(1.5\)
2. \(1.75\)
3. \(2.0\)
4. \(2.5\)
Subtopic: Prisms |
75%
Level 2: 60%+
Hints
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