When an object is placed at the principal focus of a concave mirror, the location of the image formed is

Analyze the question: The object is placed exactly at the principal focus (F) of a concave mirror. We need to know where the image forms.

Concept: For a concave mirror, the mirror formula is:

1/f = 1/u + 1/v

where f is the focal length, u is the object distance and v is the image distance.

Solution:

Since the object is at the principal focus, u = f.

1/f = 1/f + 1/v

1/v = 1/f − 1/f = 0

So v = 1/0, which means v → ∞.

Ray diagram reasoning: Rays from a point at F strike the mirror and reflect parallel to the principal axis. Parallel rays never meet, so they meet only "at infinity". The image is therefore:

• at infinity
• real (in the sense of being formed by reflected rays), highly magnified, and inverted

This is the reverse of the situation where parallel rays from a distant object converge at F. Reflected rays can retrace the same path in reverse. This is how a torch, car headlight or search light works. The bulb sits at the focus of a concave reflector to produce a parallel beam.

Checking the options:

• A. Between F and pole: this occurs when the object is between F and the pole (a virtual image). ✗
• B. Between F and C: this occurs when the object is between F and C... actually when the object is beyond C. ✗
• C. At infinity: correct ✓
• D. At centre of curvature: this occurs when the object is at C. ✗

Answer: C. At infinity

Tip: Remember "Object at F → rays go out parallel → image at infinity." Also, "Object at C → image at C" and "Object at infinity → image at F." These three cases come up often in WASSCE and JAMB.