physics : class12 Numerical problems on lens combinations : Combination of Thin Lenses in Contact : Optics MCQ Questions and Answers
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Numerical problems on lens combinations
MCQ questions and answers.
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MCQ Questions
1. Two convex lenses of focal lengths 20 cm and 30 cm are placed in contact. What is the focal length of the combination?
A.
10 cm
B.
12 cm
C.
25 cm
D.
50 cm
Correct Answer:
12 cm
Explanation:
For lenses in contact, 1/F = 1/f1 + 1/f2. Thus, 1/F = 1/20 + 1/30 = 1/12, so F = 12 cm.
2. Two thin lenses having powers +2 D and +3 D are placed in contact. What is the power of the combination?
A.
+1 D
B.
+5 D
C.
-1 D
D.
+6 D
Correct Answer:
+5 D
Explanation:
The power of lenses in contact is the sum of their powers: P = P1 + P2 = 2 D + 3 D = +5 D.
3. A convex lens of focal length 10 cm is placed in contact with a concave lens of focal length 20 cm. What is the focal length of the combination?
A.
20 cm
B.
40 cm
C.
-20 cm
D.
-40 cm
Correct Answer:
20 cm
Explanation:
Using sign convention, f1 = +10 cm and f2 = -20 cm. Therefore, 1/F = 1/10 - 1/20 = 1/20, giving F = +20 cm.
4. Two lenses in contact have powers +4 D and -1 D. What is the power of the combination?
A.
+5 D
B.
+3 D
C.
-3 D
D.
-5 D
Correct Answer:
+3 D
Explanation:
The combined power is P = P1 + P2 = +4 D + (-1 D) = +3 D.
5. Two identical convex lenses, each having focal length 20 cm, are placed in contact. What is the focal length of the combination?
A.
10 cm
B.
20 cm
C.
40 cm
D.
5 cm
Correct Answer:
10 cm
Explanation:
For identical lenses in contact, their powers add. Hence, 1/F = 1/20 + 1/20 = 1/10, so the combined focal length is 10 cm.
6. A lens combination in contact has a power of +5 D. What is its focal length?
A.
5 cm
B.
10 cm
C.
20 cm
D.
50 cm
Correct Answer:
20 cm
Explanation:
Focal length in metres is F = 1/P = 1/5 m = 0.2 m = 20 cm.
7. A convex lens of focal length 25 cm is placed in contact with another convex lens of focal length 50 cm. What is the power of the combination?
A.
+2 D
B.
+4 D
C.
+6 D
D.
-6 D
Correct Answer:
+6 D
Explanation:
The powers are P1 = 1/0.25 = +4 D and P2 = 1/0.50 = +2 D. Therefore, the combined power is +4 D + +2 D = +6 D.
8. A convex lens of focal length 15 cm and a concave lens of focal length 30 cm are placed in contact. What is the focal length of the combination?
A.
+30 cm
B.
-30 cm
C.
+15 cm
D.
-15 cm
Correct Answer:
+30 cm
Explanation:
Taking f1 = +15 cm and f2 = -30 cm, 1/F = 1/15 - 1/30 = 1/30. Hence, F = +30 cm.
9. Two lenses of powers +3 D and +2 D are in contact. An object is placed 30 cm in front of the combination. What is the focal length of the combination?
A.
10 cm
B.
20 cm
C.
25 cm
D.
50 cm
Correct Answer:
20 cm
Explanation:
The combined power is 3 D + 2 D = 5 D. Therefore, F = 1/5 m = 0.2 m = 20 cm. The object distance does not affect the focal length.
10. A combination of two lenses in contact has focal length 50 cm. One lens has focal length 25 cm. What is the focal length of the second lens?
A.
25 cm
B.
50 cm
C.
75 cm
D.
100 cm
Correct Answer:
50 cm
Explanation:
Using 1/F = 1/f1 + 1/f2, 1/50 = 1/25 + 1/f2. Thus, 1/f2 = 1/50 - 1/25 = -1/50, so f2 = -50 cm. Since the available option represents the magnitude, the second lens has focal length 50 cm and is concave.
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