What is the focal length of the mirror?

Correct answer: a 7.5 m

u = 5 m, and the image is virtual so v = −3 m. 1/f = 1/u + 1/v = 1/5 − 1/3 = −2/15, so f = −7.5 m. The minus sign means the mirror is convex; the focal length is 7.5 m.

Why the other options are wrong

• b 1.875 m: This is not the answer: 1.875 = (5 × 3) ÷ (5 + 3): this comes from taking v as positive. For a virtual image v is negative.
• c 0.533 m: This is not the answer: 0.533 is the value of 1/5 + 1/3 = 8/15, that is 1/f; it has to be inverted to get the focal length, and v has to be taken as negative.
• d 0.133 m: This is not the answer: 0.133 is the size of 1/5 − 1/3 = −2/15 (1/f); that is not the focal length but its reciprocal.