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A real object is placed at a distance f from the pole of a convex mirror, in front of the convex mirror. If the focal length of the mirror is f, then the distance of the image from the pole of the mirror is ________.

Asked in GUJCET 2009 · Mirror formula and magnification

• (1) f/2
• (2) f/4
• (3) 2f
• (4) 4f

Step-by-step solution

Why the other options are wrong

• (2) No sign convention gives f/4: it is the correct f/2 halved a second time. Sanity check: 1/v=1/f-1/(-f)=2/f, so v=f/2.
• (3) 2f is the mirror's radius of curvature R, quoted in place of the image distance. In a convex mirror the virtual image always lies between the pole and the focus, so v<f; here 1/v=2/f gives v=f/2.
• (4) 4f is twice the radius of curvature. A convex mirror's image can never be further behind the pole than its focus, so v<f whatever the object distance.

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