What is the magnification produced by a concave lens of focal length 10 cm, when an image is formed at a distance of 5 cm from the lens?
- A.2.0
- B.1.0
- C.0.5
- D.0.33
Correct answer
Explanation
The correct answer is C, 0.5. Using the lens formula with sign conventions, the object is found to be 10 cm from the lens, and the magnification v/u comes to 0.5. For a concave lens, the focal length is negative, so f = −10 cm, and its image is always virtual and on the same side as the object, so v = −5 cm. The lens formula is 1/v − 1/u = 1/f. Substituting, −1/5 − 1/u = −1/10, which gives 1/u = −1/10, so u = −10 cm. Magnification for a lens is m = v/u = (−5)/(−10) = +0.5. The positive sign means an erect image; a value below one means a diminished one. Option A is wrong because a magnification of 2 would mean an enlarged image, which a concave lens never forms. Option B is wrong because a magnification of 1 would mean an image of the same size, which happens only for an object at the lens itself. Option D is wrong because 0.33 would need v to be a third of u, not half. Exam tip: a concave lens always gives a virtual, erect and diminished image, so 0 < m < 1.
Practice Questions
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- C.Speed is vector quantity and velocity is scalar quantity.
- D.Speed is scalar quantity and velocity is vector quantity.
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