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Q. No.
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. \(-2:1\)
Subtopic:  Lenses |
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 convex lens of focal length \(60\) cm is placed in the path of a parallel beam, falling parallel to its principal axis. A plane mirror is placed on the principal axis, making an angle of \(45^{\circ}\) with it, at a distance of \(30\) cm behind the lens. The distance of the new focus from lens (optical centre) is:
1. \(60\) cm
2. \((60+30\sqrt2)\) cm
3. \(60\sqrt2\) cm
4. \(30\sqrt2\) cm
Subtopic:  Lenses |
Level 3: 35%-60%
Hints
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An equiconvex lens of focal length \(100\) cm is split into two plano-convex lenses and the plane surface of one of these lenses is silvered. This acts as a:
1. converging mirror of focal length \(200\) cm.
2. converging mirror of focal length \(100\) cm.
3. diverging mirror of focal length \(200\) cm.
4. diverging mirror of focal length \(100\) cm.
Subtopic:  Lenses |
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. \(1.2\)
Subtopic:  Lenses |
Level 3: 35%-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, 
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
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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
Subtopic:  Lenses |
 52%
Level 3: 35%-60%
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
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