A concave mirror produces 3 times magnified real image of an object placed at 10 cm in front of it. Where is image? Use LaTex

To determine the location of the image produced by a concave mirror, we can use the mirror equation and the magnification formula.

### Given:
- Object distance (\( u \)) = -10 cm (the object distance is taken as negative according to the sign convention for mirrors)
- Magnification (\( m \)) = -3 (since the image is real and inverted, the magnification is negative)

### Magnification formula:
\[
m = \frac{-v}{u}
\]
where:
- \( v \) is the image distance.
- \( u \) is the object distance.

Substituting the known values:
\[
-3 = \frac{-v}{-10}
\]

\[
v = 30 \text{ cm}
\]

Thus, the image is formed at a distance of \( \mathbf{30 \, \text{cm}} \) in front of the mirror (on the same side as the object).

Would you like more details or have any questions? Here are some related questions:

1. What is the significance of a negative magnification in mirrors?
2. How does the sign convention for mirrors differ from that of lenses?
3. What would be the image distance if the magnification was 2 instead of 3?
4. How does the focal length of the mirror relate to the object and image distances?
5. What changes if the image formed is virtual rather than real?
6. How would the image distance change if the object is moved closer to the mirror?
7. Can a concave mirror ever produce a magnification less than 1? Explain.
8. How does the radius of curvature of the mirror affect the image formation?

**Tip:** Always remember to use the correct sign convention for mirrors when solving problems involving mirrors. This will help you avoid common errors.

Explore how a concave mirror produces a real image three times magnified from an object placed 10 cm in front of it. Understand the mirror equation and magnification formula to determine the image location. Suitable for high school students studying optics and geometric optics.

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