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:
1. \(2~\text{cm}\) 2. \(20~\text{cm}\)
3. \(115~\text{cm}\) 4. \(230~\text{cm}\)
Subtopic:  Lenses |
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\(AB\) 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 |
 52%
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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. \(0.7~\text{mm}\)
Subtopic:  Lenses |
 68%
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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, 
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 |
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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 |
 71%
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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 |
 74%
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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:
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%
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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 |
 55%
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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, 
                         
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 |
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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:  Reflection at Spherical Surface |
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