An object is placed 15 cm in front of a convex lens of focal length 25 cm. The image distance will be .
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A.
−10.0 cm
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B.
−37.5 cm
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C.
−9.37 cm
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D.
17.5 cm
Correct Answer:
B. −37.5 cm
Explanation:
To find the image distance for an object placed 15 cm in front of a convex lens with a focal length of 25 cm, we use the lens formula: 1/f = 1/v - 1/u. Given the focal length (f) is +25 cm and the object distance (u) is -15 cm (following sign convention), the equation becomes 1/25 = 1/v - 1/(-15), which simplifies to 1/25 = 1/v + 1/15. Solving for 1/v gives 1/v = 1/25 - 1/15. Finding a common denominator, 1/v = (3 - 5) / 75, which results in 1/v = -2/75. Therefore, the image distance (v) is -37.5 cm. The negative sign indicates that a virtual, upright image is formed on the same side as the object.
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