A concave lens forms an image at a distance of 20cm from the lens when an object is placed at a distance of 30cm from the lens. Calculate the power of the lens
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A.
(5/3)D
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B.
(-5/3)D
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C.
(3/5)D
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D.
(-3/5)D
Correct Answer:
B. (-5/3)D
Explanation:
A concave lens always forms a virtual and erect image on the same side as the object, meaning both the object distance (u) and image distance (v) are negative according to sign convention. Given u = -30 cm and v = -20 cm, the lens formula (1/f = 1/v - 1/u) gives 1/f = 1/(-20) - 1/(-30), which simplifies to 1/f = -1/20 + 1/30 = -1/60. Thus, the focal length (f) is -60 cm or -0.6 meters. Since power (P) is the reciprocal of the focal length in meters (P = 1/f), the calculation is P = 1/(-0.6), resulting in -5/3 D.
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