An object is placed 15cm in front of a concave mirror of focal length 20cm. The image formed is

Analyze the question: An object is placed 15 cm from a concave mirror with focal length 20 cm. Since the object distance (15 cm) is less than the focal length (20 cm), the object is between the pole (P) and the principal focus (F).

Concept: Use the mirror formula (real-is-positive convention):

1/f = 1/u + 1/v

and magnification m = v/u (taking magnitudes, with sign showing the nature of the image).

Solution:

• f = +20 cm, u = +15 cm
• 1/v = 1/f − 1/u = 1/20 − 1/15
• 1/v = (3 − 4)/60 = −1/60
• v = −60 cm

The negative sign means the image is virtual, formed 60 cm behind the mirror.

Magnification: m = −v/u = −(−60)/15 = +4

• The positive sign means the image is erect.
• The value 4 (greater than 1) means the image is magnified (4 times larger).

Answer: The image is virtual, erect and magnified, which matches option D.

Tip: For a concave mirror, remember the rule:

• Object beyond F: the image is real and inverted.
• Object between P and F: the image is virtual, erect and magnified. This is how a shaving mirror or makeup mirror works.

Just compare the object distance with the focal length first. If u < f, you immediately know the answer is virtual, erect and magnified.