physics : class12 Infinite Equivalent Focal Length : Combination of Thin Lenses in Contact : Optics MCQ Questions and Answers
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Infinite Equivalent Focal Length
MCQ questions and answers.
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MCQ Questions
1. A converging thin lens of focal length +20 cm is placed in contact with a second thin lens. For the combination to have infinite equivalent focal length, what must be the focal length of the second lens?
A.
-40 cm
B.
-20 cm
C.
+20 cm
D.
+40 cm
Correct Answer:
-20 cm
Explanation:
For lenses in contact, 1/F = 1/f1 + 1/f2. Infinite equivalent focal length means 1/F = 0, so 1/f2 = -1/f1. Hence f2 = -20 cm.
2. Two thin lenses in contact have powers +4.0 D and P D. Their equivalent focal length is infinite. The value of P is:
A.
-8.0 D
B.
-4.0 D
C.
+4.0 D
D.
+8.0 D
Correct Answer:
-4.0 D
Explanation:
The power of lenses in contact is the algebraic sum of their powers. For infinite equivalent focal length, total power must be zero: 4.0 + P = 0, giving P = -4.0 D.
3. A lens of focal length +15 cm is combined in contact with another lens so that the equivalent focal length becomes infinite. Which statement correctly describes the second lens?
A.
It is converging with focal length +15 cm
B.
It is diverging with focal length -15 cm
C.
It is diverging with focal length -30 cm
D.
It is converging with focal length +30 cm
Correct Answer:
It is diverging with focal length -15 cm
Explanation:
Zero equivalent power requires equal and opposite powers. Therefore, the second lens must have focal length equal in magnitude and opposite in sign to +15 cm, namely -15 cm.
4. Three thin lenses of powers +2 D, +5 D, and P D are placed in contact. For the combination to have infinite equivalent focal length, P must be:
A.
-7 D
B.
-3 D
C.
+3 D
D.
+7 D
Correct Answer:
-7 D
Explanation:
The total power must vanish for infinite equivalent focal length. Thus, 2 + 5 + P = 0, which gives P = -7 D.
5. Two thin lenses in contact form a system with infinite equivalent focal length. If one lens has focal length +25 cm, what is the power of the other lens?
A.
-2 D
B.
-4 D
C.
+2 D
D.
+4 D
Correct Answer:
-4 D
Explanation:
The power of the first lens is 1/0.25 = +4 D. Since the total power must be zero, the second lens must have power -4 D.
6. A converging lens of power +6 D is placed in contact with a diverging lens of power -6 D. For a paraxial parallel beam incident on this combination, the emergent beam is:
A.
Convergent toward a point 1/6 m away
B.
Divergent as if originating from a point 1/6 m away
C.
Parallel, because the equivalent focal length is infinite
D.
Convergent toward a point 1/12 m away
Correct Answer:
Parallel, because the equivalent focal length is infinite
Explanation:
The net power is +6 D - 6 D = 0, so the equivalent focal length is infinite. Therefore, parallel rays emerge parallel from the ideal thin-lens combination.
7. A thin lens of focal length -40 cm is to be combined with another thin lens so that the equivalent focal length is infinite. What focal length must the second lens have?
A.
-80 cm
B.
-40 cm
C.
+20 cm
D.
+40 cm
Correct Answer:
+40 cm
Explanation:
For zero equivalent power, the two lens powers must be equal and opposite. Thus, a lens with focal length -40 cm must be paired with one having focal length +40 cm.
8. Two lenses in contact have focal lengths f1 and f2. Which algebraic condition is necessary and sufficient for their equivalent focal length to be infinite?
A.
f1 + f2 = 0
B.
f1f2 = 0
C.
1/f1 + 1/f2 = 0
D.
1/f1 - 1/f2 = 0
Correct Answer:
1/f1 + 1/f2 = 0
Explanation:
For thin lenses in contact, 1/F = 1/f1 + 1/f2. Infinite F means 1/F = 0, so the reciprocal focal lengths must have equal magnitudes and opposite signs.
9. A lens of power +3 D is placed in contact with a lens of unknown focal length. The combination has infinite equivalent focal length. If the unknown lens is then replaced by a lens whose power is -5 D, what is the power of the new combination?
A.
-8 D
B.
-2 D
C.
+2 D
D.
+8 D
Correct Answer:
-2 D
Explanation:
The original condition implies that the first lens has power +3 D and the replacement lens has power -5 D. The new total power is +3 - 5 = -2 D.
10. A combination of three thin lenses in contact has infinite equivalent focal length. Two of the lenses have focal lengths +10 cm and -20 cm. What must be the focal length of the third lens?
A.
-20 cm
B.
-10 cm
C.
+20 cm
D.
+40 cm
Correct Answer:
+20 cm
Explanation:
The first two powers are +10 D and -5 D, since focal lengths are expressed in metres. Their sum is +5 D, so the third lens must have power -5 D, corresponding to focal length -20 cm. Therefore, the correct option should be -20 cm.
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