What condition is necessary for a real image to be produced in a concave mirror?

Question

BlackTom AI · Accepted Answer

For a concave mirror, real images form when reflected rays actually converge to meet in front of the mirror — this requires the object to be placed beyond the mirror’s focal point. 1) Relevant knowledge points and concepts - Mirror equation: 1/f = 1/do + 1/di (f = focal length, do = object distance, di = image distance). - Sign convention for a concave mirror: f > 0. A positive di means the image is real (located in front of the mirror). A negative di means the image is virtual (behind the mirror). - Magnification: m = -di/do. A real image is inverted (m negative); its size relative to the object depends on |m|. 2) Step-by-step reasoning - Rearrange the mirror equation to solve for di: 1/di = 1/f − 1/do. - The sign of di depends on the sign of (1/f − 1/do) = (do − f)/(f·do). - If do > f, then (do − f) > 0 so 1/di > 0 and di > 0 → image is real. - If do < f, then (do − f) < 0 so 1/di < 0 and di < 0 → image is virtual. 3) Calculations (examples) - Example 1: f = 10 cm, do = 20 cm (> f). 1/di = 1/10 − 1/20 = (2 − 1)/20 = 1/20 → di = 20 cm (positive → real). m = −20/20 = −1 (inverted, same size). - Example 2: f = 10 cm, do = 5 cm (< f). 1/di = 1/10 − 1/5 = (1 − 2)/10 = −1/10 → di = −10 cm (negative → virtual). 4) Why the correct answer is correct - From the mirror equation and sign rules, only when the object is beyond the focal point (do > f) does di become positive, meaning reflected rays converge in front of the mirror and produce a real image. 5) Why the other options are incorrect - a. “Object smaller than its image” is not necessary — size depends on do and can be smaller or larger; not a criterion for reality. - c. “Object larger than its image” likewise is not required; image size varies with object distance. - d. “Object closer than the mirror than the focal point” (do < f) produces a virtual (not real) image located behind the mirror. 6) Conclusion The necessary condition for a real image in a concave mirror is that the object be beyond the focal point; this matches the given correct answer: b. The object needs to be beyond the focal point.

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