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Q. No.A convex lens forms a real image of the same size as that of the object, but when it is moved closer by \(15~\text{cm}\) it forms a real image that is twice as large. The focal length of the lens is:
1. \(15~\text{cm}\)
2. \(30~\text{cm}\)
3. \(45~\text{cm}\)
4. \(90~\text{cm}\)
Subtopic: Lenses |
72%
Level 2: 60%+
Hints
Two parallel mirrors \(M_1\) and \(M_2\) are placed facing each other on opposite sides of a room. The separation of the mirrors, as shown in the figure below, is \(4~\text{m}.\) A point object \(P\) is placed at a distance of \(1~\text{m}\) from \(M_1.\) The separation between the images formed after a single reflection is:
| 1. | \(2~\text{m}\) | 2. | \(6~\text{m}\) |
| 3. | \(8~\text{m}\) | 4. | \(4~\text{m}\) |
Subtopic: Reflection at Plane Surface |
75%
Level 2: 60%+
Hints
A ray of light passes through three parallel media, with the angles of incidence and emergence as shown in the figure. The refractive indices of the media are \(\mu_{1}\) = 1, \(\mu_{2}\) and \(\mu_{3}\).
Then:
Then:
| 1. | \(\mu_{2}=\dfrac{1}{3},~\mu_{3}=\dfrac{1}{2}\) | 2. | \(\mu_{2}=3,~\mu_{3}=\dfrac{3}{2}\) |
| 3. | \(\mu_{2}=\dfrac{1}{3},~\mu_{3}=\dfrac{2}{3}\) | 4. | \(\mu_{2}=3,~\mu_{3}=2\) |
Subtopic: Refraction at Plane Surface |
80%
Level 1: 80%+
Hints
A thin equi-convex lens of refractive index \(1.2\) is dipped in oil of index \(1.44.\) The lens has a power of \(2\) D (in air). When it is immersed in the oil, the focal length of the lens becomes:
| 1. | \(50\) cm | 2. | \(-50\) cm |
| 3. | \(-50/1.2\) cm | 4. | \(-50 \times1.2\) cm |
Subtopic: Lens Makers' Formula |
56%
Level 3: 35%-60%
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: Reflection at Plane Surface |
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 the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Reflection at Spherical Surface |
Level 4: Below 35%
Hints
A small object is placed on the principal axis of a convex lens and it forms a real image with a (transverse) magnification of \(2.\) If the object were to move perpendicular to the principal axis with a speed \(u,\) the speed of the image will be:
| 1. | \(u\) | 2. | \(u/2\) |
| 3. | \(2u\) | 4. | \(4u\) |
Subtopic: Reflection at Spherical Surface |
Level 3: 35%-60%
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: 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: Lenses |
58%
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: Lenses |
50%
Level 3: 35%-60%
Hints
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