An object is located 25.0 cm from a convex mirror. The image distance is -50.0 cm. What is the magnification?
The Correct Answer and Explanation is :
To calculate the magnification produced by a convex mirror, we can use the magnification formula:
[
m = -\frac{d_i}{d_o}
]
Where:
- (m) is the magnification,
- (d_i) is the image distance (negative for convex mirrors),
- (d_o) is the object distance (positive in this case).
Given Data:
- Object distance ((d_o)) = 25.0 cm (positive because the object is in front of the mirror)
- Image distance ((d_i)) = -50.0 cm (negative because the image is virtual in a convex mirror)
Calculation:
Substituting the values into the magnification formula:
[
m = -\frac{d_i}{d_o} = -\frac{-50.0 \text{ cm}}{25.0 \text{ cm}} = \frac{50.0}{25.0} = 2.0
]
Explanation:
The magnification of 2.0 indicates that the image produced by the convex mirror is upright and twice the size of the object.
Convex mirrors are known for producing virtual images that appear behind the mirror. These images are always smaller than the object and upright, which means that the magnification is positive. However, in this case, since the image distance is negative, the negative sign in the magnification formula ensures that the resulting magnification is positive, consistent with the properties of convex mirrors.
A convex mirror diverges light rays, which means they appear to originate from a point behind the mirror. This results in a virtual image that cannot be projected onto a screen. The property of producing upright images is particularly useful in applications like vehicle side mirrors, where a wider field of view is beneficial. The magnification helps us understand the relationship between the object size and the image size. In practical terms, a magnification of 2.0 means that if the object were 1 cm tall, the image would appear to be 2 cm tall when viewed in the mirror.
In summary, the calculation shows that the image formed is larger than the object, and understanding this relationship is critical in various optical applications.