An object is placed at a distance of 15 cm in front of a concave mirror with a radius of curvature of 20 cm. Which one among the following statements is correct for the image formed?
Answer
The correct answer is A: The image is 30 cm from the mirror on the same side as the object.. For a concave mirror, focal length f = R/2 = 20/2 = 10 cm. Using the mirror formula 1/v + 1/u = 1/f with the sign convention u = −15 cm and f = −10…
A.The image is 30 cm from the mirror on the same side as the object.✓ Correct
B.The image is formed at a distance of 30 cm behind the mirror.
C.The image is 60 cm from the mirror on the same side as the object.
D.The image is formed at a distance of 60 cm behind the mirror.
Explanation
For a concave mirror, focal length f = R/2 = 20/2 = 10 cm. Using the mirror formula 1/v + 1/u = 1/f with the sign convention u = −15 cm and f = −10 cm: 1/v = 1/f − 1/u = (−1/10) − (−1/15) = −1/10 + 1/15 = (−3 + 2)/30 = −1/30, so v = −30 cm. The negative sign indicates the image is formed on the same side as the object (in front of the mirror), i.e., it is a real, inverted image at 30 cm from the mirror. Hence option (a) is correct.
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