physics : class12 Experimental Determination of Power : Combination of Thin Lenses in Contact : Optics MCQ Questions and Answers
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Experimental Determination of Power
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MCQ Questions
1. In an optical-bench experiment, a combination of two thin lenses in contact forms a sharp image of a distant object at a distance of 20.0 cm from the combination. What is the experimentally determined power of the combination?
A.
+2.0 D
B.
+5.0 D
C.
-5.0 D
D.
+20.0 D
Correct Answer:
+5.0 D
Explanation:
For a distant object, the image distance gives the focal length: f = 20.0 cm = 0.20 m. Hence, P = 1/f = 1/0.20 = +5.0 D.
2. An object and a screen are separated by 100 cm. A combination of thin lenses in contact gives two sharp-image positions whose separation is 60 cm. What is the power of the combination determined by the displacement method?
A.
+4.00 D
B.
+6.25 D
C.
+8.00 D
D.
-6.25 D
Correct Answer:
+6.25 D
Explanation:
Using the displacement method, f = (D² − d²)/(4D) = (100² − 60²)/(4 × 100) cm = 16 cm = 0.16 m. Therefore, P = 1/0.16 = +6.25 D.
3. In the displacement method, the distance between the object and screen is 90 cm and the separation between the two sharp-image positions is 30 cm. What focal length and power are obtained for the lens combination?
A.
20 cm and +5.0 D
B.
15 cm and +6.67 D
C.
22.5 cm and +4.44 D
D.
30 cm and +3.33 D
Correct Answer:
20 cm and +5.0 D
Explanation:
The focal length is f = (D² − d²)/(4D) = (90² − 30²)/(4 × 90) cm = 20 cm. Thus, P = 1/0.20 = +5.0 D.
4. While experimentally determining the focal length of a lens combination using several object and image positions, a graph of 1/v against 1/u is plotted using Cartesian sign convention. What does the intercept on the 1/v axis represent?
A.
The power of the combination in dioptres
B.
The focal length of the combination in metres
C.
The reciprocal of the focal length, equal to its power
D.
The magnification produced by the combination
Correct Answer:
The reciprocal of the focal length, equal to its power
Explanation:
From the lens formula, 1/v = 1/u + 1/f. Therefore, the intercept on the 1/v axis is 1/f, which is the power P when f is expressed in metres.
5. A known converging lens of power +2.0 D is placed in contact with an unknown lens. The focal length of the combination is experimentally found to be 1.00 m. What is the power of the unknown lens?
A.
+0.5 D
B.
-1.0 D
C.
-2.0 D
D.
+3.0 D
Correct Answer:
-1.0 D
Explanation:
For lenses in contact, powers add: P_combination = P_known + P_unknown. Since P_combination = 1/1.00 = +1.0 D, P_unknown = +1.0 − (+2.0) = −1.0 D.
6. For an optical-bench determination using the displacement method, the object-screen distance is D and the separation of the two sharp-image positions is d. Which measured quantity is most sensitive to a small absolute error in d when d is close to D?
A.
The focal length calculated from f = (D² − d²)/(4D)
B.
The optical power calculated from P = 1/f
C.
The object-screen distance D, because it is squared
D.
The magnification, because it is independent of d
Correct Answer:
The optical power calculated from P = 1/f
Explanation:
When d approaches D, the calculated focal length becomes small. Since power is the reciprocal of focal length, even a small uncertainty in d can produce a relatively large fractional uncertainty in f and hence an especially large fractional uncertainty in P.
7. In an experiment using the displacement method, the object and screen are fixed 80 cm apart. If the focal length of the lens combination is 20 cm, what should be observed for the two sharp-image positions?
A.
Two positions separated by 40 cm
B.
Two positions separated by 20 cm
C.
The two positions coincide
D.
No sharp image can be obtained at any position
Correct Answer:
The two positions coincide
Explanation:
For two distinct positions, D must exceed 4f. Here D = 80 cm and 4f = 80 cm, so d = √(D² − 4Df) = 0. Thus, the two conjugate positions merge into one.
8. A lens combination gives the following readings in an optical-bench experiment: object distance u = −30 cm and image distance v = +60 cm. What power is obtained from this observation?
A.
+3.33 D
B.
+5.00 D
C.
-5.00 D
D.
+7.50 D
Correct Answer:
+5.00 D
Explanation:
Using 1/f = 1/v − 1/u, 1/f = 1/60 − (−1/30) = 1/20 cm⁻¹. Hence f = 20 cm = 0.20 m and P = +5.00 D.
9. A student determines the focal length of a lens combination by measuring several pairs of conjugate distances and obtains f values of 19.8 cm, 20.1 cm, 20.0 cm, and 20.2 cm. What is the best reported power, ignoring instrumental resolution beyond the given data?
A.
+4.80 D
B.
+4.95 D
C.
+5.03 D
D.
+5.20 D
Correct Answer:
+5.03 D
Explanation:
The mean focal length is (19.8 + 20.1 + 20.0 + 20.2)/4 = 20.025 cm = 0.20025 m. Therefore, P = 1/0.20025 ≈ +5.03 D.
10. A combination of two lenses in contact has one lens of power +4.0 D. In the experiment, the combination is found to have a focal length of 50 cm. Which power must the second lens have?
A.
-4.0 D
B.
-2.0 D
C.
+2.0 D
D.
+6.0 D
Correct Answer:
-2.0 D
Explanation:
The experimentally measured combination power is P = 1/0.50 = +2.0 D. Since powers of lenses in contact add, the second lens has P₂ = +2.0 − +4.0 = −2.0 D.
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