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?

To find the image location in a concave mirror, you can use the mirror formula:

1/f = 1/d_0 + 1/d₁

Where:

» f is the focal length of the mirror (positive for concave mirrors),
» d_o is the object distance (distance from the object to the mirror)
» d₁ is the image distance (distance from the image to the mirror).
Given that the concave mirror produces a magnified (enlarged) real image, the magnification (m) is positive and given by the formula:

m = – d₁/d_0

In this case, you’re told that the magnification is 3, so m = 3.

Also, the object distance (d_0) is 10 cm.
Now, let’s find the image distance (d₁) using the magnification formula:
3 = −d₁/10
​
Solving for d₁:
d₁= − 30 cm

The negative sign indicates that the image is formed on the same side as the object (in front of the mirror). So, the real and magnified image is located 30cm in front of the concave mirror.