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?
- A.The image is 30 cm from the mirror on the same side as the object.
- 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.
Correct answer
Explanation
The correct answer is A, The image is 30 cm from the mirror on the same side as the object. The focal length is 10 cm, and an object between F and C of a concave mirror gives a real image beyond C, in front of the mirror.
The focal length is half the radius of curvature: f = 20/2 = 10 cm, taken as −10 cm by the sign convention, with u = −15 cm. The mirror formula 1/v + 1/u = 1/f gives 1/v = −1/10 + 1/15 = −1/30, so v = −30 cm. The negative sign means the image is on the same side as the object, so it is real. The magnification m = −v/u = −2, so the image is inverted and twice the size of the object.
B is wrong: an image behind a concave mirror is virtual and forms only when the object is inside the focus (u less than 10 cm).
C is wrong: 60 cm is the result of using the radius (20 cm) as if it were the focal length.
D is wrong: the distance and the side are both wrong; v is −30 cm.
Exam tip: concave mirror, object between F and C → real, inverted, enlarged image beyond C; f = R/2.
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