An object is placed 25cm in front of a convex mirror has its image formed 5cm behind the mirror. what is the focal length of the convex mirror

Analyze the question

A convex mirror always forms a virtual, upright, diminished image behind the mirror. We're given the object distance and the image distance, and we need the focal length.

Concept

Mirror formula:

1/f = 1/u + 1/v

Using the real-is-positive convention:

• Object distance u = +25 cm (real object in front)
• Image distance v = -5 cm (virtual image behind the mirror)

For a convex mirror, f should come out negative (a virtual focus).

Solution

1/f = 1/25 + 1/(-5) 1/f = 1/25 - 5/25 1/f = -4/25

f = -25/4 = -6.25 cm

The negative sign shows the focus is virtual, which is what we expect for a convex mirror. The magnitude of the focal length is 6.25 cm.

Check: The image is closer to the mirror than the focus, which is consistent with a virtual image. Magnification = v/u = 5/25 = 0.2, so the image is diminished, as a convex mirror should give.

Answer: Option B (6.25 cm).

Exam tip: In convex mirror problems, the image distance is always taken as negative in the real-is-positive convention. If you ever get a positive f for a convex mirror, you have made a sign error. Also remember that 1/25 - 1/5 simplifies fast if you convert to a common denominator of 25.