Chapter 9 · Question 6

A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?

Answer Revealed

Direct Answer:

Using the magnification formula

m = -v/u

, with

m = -3

(real image),

u = -10

cm, we get

-3 = -v/(-10)

, so

v = -30

cm. The image is located 30 cm in front of the mirror.

Simple Explanation

Since the image is real and 3 times bigger, it forms on the same side as the object. Using the magnification formula, the image distance works out to 30 cm in front of the mirror.

Exam-Ready Structure

Given: Magnification (

m

) = -3 (negative because image is real and inverted). Object distance (

u

) = -10 cm (negative by sign convention, object is in front of the mirror). Using the magnification formula:

m = h'/h = -v/u

. Substituting:

-3 = -v/(-10)

-3 = v/10

v = -30

cm. The negative sign indicates that the image is formed in front of the mirror (on the same side as the object), which is consistent with a real image. Answer: The image is located 30 cm in front of the concave mirror.

Key Points

For a real image, magnification is negative: $m = -3$
Object distance is negative by sign convention: $u = -10$ cm
Using $m = -v/u$ : $v = -30$ cm
Image is 30 cm in front of the mirror

A concave mirror produces three times magnified (enlarged) real image of an object placed at 10 cm in front of it. Where is the image located?