A concave mirror produces a magnified, real image of an object placed 10 cm in front of it. This implies that the image distance (v) is:

Steps to Solve

1. Identify the mirror formula The mirror formula relates the object distance ($u$), the image distance ($v$), and the focal length ($f$). The formula is given by:

$$ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} $$

2. Determine the object distance The problem states that the object is placed 10 cm in front of the mirror. In mirror conventions, we take the object distance ($u$) as negative:

$$ u = -10 , \text{cm} $$

3. Set the focal length For a concave mirror, the focal length ($f$) is positive. Assuming a focal length of 5 cm (this can depend on the specific mirror), we use:

$$ f = 5 , \text{cm} $$

4. Substitute known values into the mirror formula Now, we substitute the values of $f$ and $u$ into the mirror formula:

$$ \frac{1}{5} = \frac{1}{-10} + \frac{1}{v} $$

5. Solve for image distance ($v$) Rearranging to isolate $\frac{1}{v}$ gives us:

$$ \frac{1}{v} = \frac{1}{5} + \frac{1}{10} $$

Calculating the right-hand side:

$$ \frac{1}{v} = \frac{2}{10} + \frac{1}{10} = \frac{3}{10} $$

Thus, we have:

$$ v = \frac{10}{3} \approx 3.33 , \text{cm} $$

6. Determine the nature of the image Since the value of $v$ is positive, this indicates that the image is real and located on the same side as the object.