To find the magnification of the object placed in front of a convex mirror, we can use the formula for magnification \( m \) in the context of mirrors:

\(m = \frac{h'}{h} = \frac{-v}{u}\)

where:

• \( h' \) is the height of the image.
• \( h \) is the height of the object.
• \( v \) is the image distance.
• \( u \) is the object distance (given as -10 cm since the object is on the left side of the mirror, according to the sign convention for mirrors).

For a convex mirror, the focal length \( f \) is positive. Given: \( f = 15 \, \text{cm} \) and \( u = -10 \, \text{cm} \).

Using the mirror formula,

\(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)

Substitute the values:

\(\frac{1}{15} = \frac{1}{v} + \frac{1}{-10}\)

Rearrange to solve for \( \frac{1}{v} \):

\(\frac{1}{v} = \frac{1}{15} + \frac{1}{10}\)

Calculate the right-hand side:

\(\frac{1}{v} = \frac{2}{30} + \frac{3}{30} = \frac{5}{30} = \frac{1}{6}\)

Therefore,

\(v = 6 \, \text{cm}\)

Now calculate the magnification \( m \):

\(m = \frac{-v}{u} = \frac{-6}{-10} = +0.6\)

Hence, the magnification of the object by the convex mirror is +0.6.

Let's validate the options given in the question:

• +0.3 - Incorrect. This does not match the computed magnification.
• +0.6 - Correct. This matches the computed magnification.
• -0.3 - Incorrect. The sign is wrong and does not match the computed magnification.
• -0.6 - Incorrect. The sign is wrong and does not match the computed magnification.