An object is placed 20cm from a concave mirror of focal length 10cm. The linear magnification of the image produced is?

Analyze the question: An object is 20 cm from a concave mirror with focal length 10 cm. We need the linear magnification.

Concept: Use the mirror formula:

1/f = 1/u + 1/v

and magnification:

m = v/u (in magnitude; the negative sign only shows the image is inverted)

Solution:

Given: f = 10 cm, u = 20 cm (real-is-positive convention)

1/v = 1/f − 1/u 1/v = 1/10 − 1/20 1/v = 2/20 − 1/20 = 1/20

v = 20 cm

Magnification:

m = v/u = 20/20 = 1

So the image is the same size as the object (magnification of magnitude 1). It is real and inverted, formed at 20 cm, which is the centre of curvature (since R = 2f = 20 cm). An object placed at C always gives an image at C, the same size as the object.

Answer: The magnification is 1, which is option C.

Tip: Remember the special cases for a concave mirror:

• Object at C (u = 2f): image at C, real, inverted, same size, so m = 1
• Object at F: image at infinity
• Object between F and C: image beyond C, magnified

Whenever u = 2f, you can immediately say m = 1 without calculating.