physics : class12 Image formation by equivalent lens : Combination of Thin Lenses in Contact : Optics MCQ Questions and Answers
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Image formation by equivalent lens
MCQ questions and answers.
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MCQ Questions
1. Two thin converging lenses of focal lengths 20 cm and 30 cm are placed in contact. An object is placed 24 cm in front of the combination. Where is the image formed?
A.
12 cm in front of the combination
B.
24 cm behind the combination
C.
36 cm behind the combination
D.
At infinity
Correct Answer:
24 cm behind the combination
Explanation:
The equivalent focal length is 1/F = 1/20 + 1/30, so F = 12 cm. For u = -24 cm, the lens formula gives v = 24 cm. The positive value indicates that the image is formed 24 cm behind the combination.
2. Two thin lenses of focal lengths +20 cm and -20 cm are placed in contact. An object is placed in front of this combination. Where is its image formed?
A.
At the equivalent focal point
B.
At twice the equivalent focal length
C.
At infinity
D.
On the object itself
Correct Answer:
At infinity
Explanation:
The equivalent power is zero because the powers of the two lenses cancel. Thus, the equivalent focal length is infinite, and parallel emergent rays indicate image formation at infinity.
3. Two converging lenses of focal lengths 10 cm and 20 cm are in contact. An object is placed 30 cm in front of them. What is the approximate image distance?
A.
5.7 cm behind the lenses
B.
8.6 cm behind the lenses
C.
15 cm behind the lenses
D.
30 cm behind the lenses
Correct Answer:
8.6 cm behind the lenses
Explanation:
The equivalent focal length is F = (10 × 20)/(10 + 20) = 6.67 cm. Using 1/F = 1/v - 1/u with u = -30 cm gives v approximately 8.6 cm, so the image is formed behind the lenses.
4. A combination of thin lenses in contact has an equivalent focal length of 15 cm. If an object is placed 30 cm in front of the combination, where is the image formed?
A.
15 cm behind the combination
B.
20 cm behind the combination
C.
30 cm behind the combination
D.
60 cm behind the combination
Correct Answer:
30 cm behind the combination
Explanation:
Using the lens formula with F = 15 cm and u = -30 cm, we get 1/15 = 1/v + 1/30, giving v = 30 cm. Therefore, the image is formed 30 cm behind the equivalent lens.
5. An equivalent converging lens has a focal length of 10 cm. An object is placed 15 cm in front of it. What is the image distance?
A.
10 cm behind the lens
B.
20 cm behind the lens
C.
30 cm behind the lens
D.
30 cm in front of the lens
Correct Answer:
30 cm behind the lens
Explanation:
For F = 10 cm and u = -15 cm, the lens formula gives 1/10 = 1/v + 1/15, so v = 30 cm. The positive image distance shows that the image is formed behind the combination.
6. A combination of lenses in contact has an equivalent focal length of -20 cm. An object is placed 30 cm in front of it. Where is the image formed?
A.
12 cm in front of the combination
B.
12 cm behind the combination
C.
20 cm in front of the combination
D.
60 cm behind the combination
Correct Answer:
12 cm in front of the combination
Explanation:
Using F = -20 cm and u = -30 cm in the lens formula gives v = -12 cm. The negative value means that the image is virtual and formed 12 cm in front of the equivalent lens.
7. Two thin lenses of powers +2 D and +3 D are placed in contact. An object is placed 0.30 m in front of the combination. Where is the image formed?
A.
0.20 m behind the combination
B.
0.30 m behind the combination
C.
0.60 m behind the combination
D.
1.00 m behind the combination
Correct Answer:
0.60 m behind the combination
Explanation:
The equivalent power is 5 D, so the equivalent focal length is 0.20 m. With u = -0.30 m, the lens formula gives v = 0.60 m. Hence, the image is formed 0.60 m behind the combination.
8. A converging lens of focal length 10 cm and a diverging lens of focal length -20 cm are placed in contact. An object is placed 40 cm in front of the combination. Where is the image formed?
A.
20 cm behind the combination
B.
40 cm behind the combination
C.
40 cm in front of the combination
D.
80 cm behind the combination
Correct Answer:
40 cm behind the combination
Explanation:
The equivalent focal length is given by 1/F = 1/10 - 1/20, so F = 20 cm. For an object at 40 cm, the lens formula gives v = 40 cm, indicating a real image 40 cm behind the combination.
9. An object is placed at the equivalent focal point of a combination of converging thin lenses in contact. Where is the image formed?
A.
At the optical centre
B.
At twice the focal length
C.
At infinity
D.
At the object position
Correct Answer:
At infinity
Explanation:
When an object is placed at the equivalent focal point, the emergent rays from the lens combination become parallel. Parallel rays meet at infinity, so the image is formed at infinity.
10. A combination of thin lenses in contact has an equivalent focal length of 20 cm. An object is placed 60 cm in front of it. What is the magnification of the image?
A.
+0.5
B.
-0.5
C.
+2
D.
-2
Correct Answer:
-0.5
Explanation:
For F = 20 cm and u = -60 cm, the lens formula gives v = 30 cm. Magnification is m = v/u = 30/(-60) = -0.5, indicating an inverted image half the size of the object.
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