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A lens is placed as shown in the figure, with the \(x\)-axis along the principal axis and the origin at the optical centre. A ray of light incident on the lens at \(P~(0, y)\) undergoes a deviation \(\delta.\) A graph of \(\delta\) vs \(y\) is shown:
The focal length of the lens is nearly:
The focal length of the lens is nearly:
| 1. | \(2~\text{cm}\) | 2. | \(20~\text{cm}\) |
| 3. | \(115~\text{cm}\) | 4. | \(230~\text{cm}\) |
Subtopic: Lenses |
Level 3: 35%-60%
Hints
\(AB\) and \(BC\) are a pair of mirrors inclined so that the angle between their planes is \(60^{\circ}\), as shown in the figure. A ray of light \(XY\) is incident on \(AB\) and emerges as the ray \(ZW\) after two reflections. If the incident ray is rotated so that \(\angle AYX\) decreases by \(15^{\circ}\), then \(\angle WZC\):
| 1. | increases by \(15^{\circ}\). | 2. | increases by \(30^{\circ}\). |
| 3. | decreases by \(15^{\circ}\). | 4. | decreases by \(30^{\circ}\). |
Subtopic: Reflection at Plane Surface |
53%
Level 3: 35%-60%
Hints
The Sun has a diameter of \(1.4\times10^6~\text{km}\) and is at a distance of \(150\times10^6~\text{km}\) from the Earth. An image of the Sun is formed by a convex lens of focal length \(30~\text{cm}.\) The diameter of the image is:
1. \(2.8~\text{cm}\)
2. \(2.8~\text{mm}\)
3. \(1.4~\text{mm}\)
4. \(0.7~\text{mm}\)
1. \(2.8~\text{cm}\)
2. \(2.8~\text{mm}\)
3. \(1.4~\text{mm}\)
4. \(0.7~\text{mm}\)
Subtopic: Lenses |
69%
Level 2: 60%+
Hints
A diverging lens (focal length of magnitude \(f_1\)) and a converging lens (focal length \(f_2\)) are placed with a common principal axis. The separation between the lenses is \(D\). A thin parallel beam of width \(d\) enters from the left and emerges as a parallel beam of width \(d'\).
Then,
Then,
| 1. | \(D=f_1+f_2,~\text{and}~d'=d\) |
| 2. | \(D=f_1-f_2,~\text{and}~d'<d\) |
| 3. | \(D=f_2-f_1,~\text{and}~d'>d\) |
| 4. | \(D=f_1+f_2,~\text{and}~d'>d\) |
Subtopic: Lenses |
Level 3: 35%-60%
Hints
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. \(90~\text{cm}\)
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
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