An object is placed 35 cm away from a convex mi... - JAMB Physics 2023 Question

To determine the location of the image formed by a convex mirror, you can use the mirror formula:

\[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \]

where:
- \( f \) is the focal length of the mirror,
- \( d_o \) is the object distance (distance of the object from the mirror),
- \( d_i \) is the image distance (distance of the image from the mirror).

Given that \( f = 15 \) cm and \( d_o = -35 \) cm (negative because it's in front of the mirror for convex mirrors), you can rearrange the formula to solve for \( d_i \):

\[ \frac{1}{d_i} = \frac{1}{f} - \frac{1}{d_o} \]

\[ \frac{1}{d_i} = \frac{1}{15} - \frac{1}{-35} \]

\[ \frac{1}{d_i} = \frac{1}{15} + \frac{1}{35} \]

\[ \frac{1}{d_i} = \frac{7}{105} + \frac{3}{105} \]

\[ \frac{1}{d_i} = \frac{10}{105} \]

\[ d_i = \frac{105}{10} \]

\[ d_i = 10.5 \, \text{cm} \]

The negative sign indicates that the image is formed on the same side as the object, which is expected for convex mirrors.

So, the correct option is 10.5 cm behind the mirror