An object 4 cm high is placed in front of a convex mirror with a focal length of 10 cm. What is the image position (in cm)?
my recommendation on these is to sketch a ray diagram, notice the position.
Then use the mirror equation...often your sign errors will be highlighted by the original ray diagram. Sign conventions for virtual images are different than usual.
To determine the image position formed by a convex mirror, we can use the mirror equation:
1/f = 1/d₀ + 1/dᵢ
Where:
f is the focal length of the mirror
d₀ is the object distance (distance of the object from the mirror)
dᵢ is the image distance (distance of the image from the mirror)
Given:
f = -10 cm (negative because it's a convex mirror)
The object distance is not provided.
In this question, we are given the height of the object (4 cm), but we need the object distance to solve for the image position.
To find the object distance, we can use the magnification formula:
m = -dᵢ / d₀
Where:
m is the magnification (in this case, the negative sign indicates that the image formed is virtual)
d₀ is the object distance
dᵢ is the image distance
Given that the height of the object (h₀) is 4 cm and the height of the image (hᵢ) is not provided, we can use the height magnification formula:
m = hᵢ / h₀
Therefore, we can rewrite the magnification formula as:
m = -dᵢ / d₀
4/d₀ = -dᵢ / d₀
Simplifying the equation:
-4 = dᵢ
Since the magnification is negative, the image formed is virtual and upright. Therefore, the image position is 4 cm in front of the mirror.
Hence, the image position is 4 cm.