Question

How far does the image of an object appear behind a convex mirror, with a focal length of 26.0 m, when the object is 10.0 m from the car?

Answer 1

The image of the object appears 16.86 meters behind the convex mirror.

Step-by-step explanation:

To determine the image distance
`(d_i)` behind a convex mirror, we can use the mirror equation:
`\((1)/(f) = (1)/(d_o) + (1)/(d_i)\)`, where
`\(f\)` is the focal length,
`\(d_o\)`is the object distance, and
`(d_i)`is the image distance. In this case, the focal length
`\(f\)` is given as 26.0 m, and the object distance
`\(d_o\)` is given as 10.0 m.

Substituting these values into the mirror equation:

`\[ (1)/(26.0) = (1)/(10.0) + (1)/(d_i) \]Now, solving for \(d_i\):\[ (1)/(d_i) = (1)/(26.0) - (1)/(10.0) \]\[ (1)/(d_i) = (10.0 - 26.0)/(260.0) \]\[ (1)/(d_i) = -(16.0)/(260.0) \]\[ d_i = -(260.0)/(16.0) \]\[ d_i \approx -16.25 \, \text{m} \]`

Since the image distance is negative, it implies that the image is formed behind the mirror. Thus, the image of the object appears approximately 16.86 meters behind the convex mirror. The negative sign indicates that the image is a virtual image formed on the same side as the incident light.