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

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