a convex mirror has a focal length of -10.0cm. what is the image position for an object that is placed l20.0cm from the mirror?
To find the image position for an object placed at a certain distance from a convex mirror, we can use the mirror formula:
1/f = 1/d₀ + 1/dᵢ
Where:
- f is the focal length of the mirror
- d₀ is the object distance from the mirror
- dᵢ is the image distance from the mirror
In this case, the focal length (f) is -10.0 cm, which indicates that the mirror is a convex mirror. The negative sign of the focal length indicates that the mirror is a diverging mirror.
Given:
- Object distance (d₀) = 120.0 cm
- Focal length (f) = -10.0 cm
We need to find the image distance (dᵢ).
Substituting the given values into the mirror formula, we have:
1/-10.0 = 1/120 + 1/dᵢ
To solve for dᵢ, we can rearrange the equation:
1/dᵢ = 1/-10.0 - 1/120
Combining the fractions on the right side:
1/dᵢ = (-120 - 10) / (-10 * 120)
1/dᵢ = -130 / (-1200)
1/dᵢ = 13 / 120
To find dᵢ, take the reciprocal of both sides:
dᵢ = 120 / 13
Therefore, the image position for an object placed 120.0 cm from the convex mirror is approximately 9.23 cm.