Concave Mirror Image Calculation

The question asks for the characteristics of an image formed by a concave mirror, given specific object placement and magnification.

Understanding Magnification and Sign Conventions

• A concave mirror is used.
• The image is real and magnified three times.
• Object distance, u, is 10 cm in front of the mirror. By convention, object distance is negative: u = -10 cm.
• Magnification, m, for a real, magnified image is negative and equals -3.

Calculating Image Distance (v)

The magnification formula for mirrors is:

$ m = -\frac{v}{u} $

Substitute the known values:

$ -3 = -\frac{v}{(-10 \text{ cm})} $

Simplify the equation:

$ -3 = \frac{v}{10 \text{ cm}} $

Solve for v:

$ v = -3 \times 10 \text{ cm} $

$ v = -30 \text{ cm} $

Interpreting the Image Characteristics

• The image distance v = -30 cm. The negative sign indicates the image is formed in front of the mirror.
• The magnification m = -3. The negative sign indicates the image is inverted. The magnitude (3) confirms it is magnified.
• A real image formed by a concave mirror is always inverted.

Therefore, an inverted image is formed at a distance of 30 cm in front of the concave mirror.