Solve the lens or mirror formula for focal length, object distance or image distance in centimetres, using the sign convention — leave one value blank.
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From the article Lens and Mirror Formula — The Sign Convention That Stops Errors.
Question: An object is placed 25 cm in front of a concave mirror of focal length 15 cm. Find the image position, nature and size.
Assign signs first: u = −25 cm, f = −15 cm (concave mirror).
Mirror formula: 1/v + 1/u = 1/f → 1/v = 1/f − 1/u
1/v = 1/(−15) − 1/(−25) = −1/15 + 1/25
Common denominator 75: −5/75 + 3/75 = −2/75
So v = −75/2 = −37.5 cm
Read the sign: v is negative, so the image is 37.5 cm in front of the mirror — a real image you could catch on a screen.
Magnification: m = −v/u = −(−37.5)/(−25) = 37.5/(−25) = −1.5
Negative → inverted. Magnitude 1.5 → one-and-a-half times taller than the object.
Sanity check: the object at 25 cm lies between f (15 cm) and 2f (30 cm), and the textbook result for that case is a real, inverted, magnified image beyond 2f. Our image is at 37.5 cm, which is indeed beyond 30 cm ✔
Worked in full in Lens and Mirror Formula — The Sign Convention That Stops Errors.
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