A negative magnification for a mirror means that A) the image is inverted, and the mirror could be either concave or convex.
B) the image is upright, and the mirror is convex. C) the image is inverted, and the mirror is convex. D) the image is inverted, and the mirror is concave. E) the image is upright, and the mirror could be either concave or convex
The Correct Answer and Explanation is :
The correct answer is D) the image is inverted, and the mirror is concave.
Explanation:
In optics, the magnification ((m)) produced by a mirror indicates the size and orientation of the image relative to the object. It is given by the formula:
[
m = -\frac{d_i}{d_o}
]
Where:
- (d_i) is the image distance (distance from the mirror to the image),
- (d_o) is the object distance (distance from the mirror to the object),
- The negative sign in the formula indicates the nature of the image (whether it is upright or inverted).
A negative magnification indicates that the image is inverted (upside down) relative to the object. This inversion happens because the image distance ((d_i)) is negative when the image forms on the opposite side of the mirror relative to the object, which typically occurs in concave mirrors.
Behavior of concave mirrors:
A concave mirror is a mirror that curves inward, resembling a portion of the interior of a sphere. These mirrors can form real or virtual images, depending on the object’s position relative to the mirror’s focal point. When the object is located outside the focal point, the image formed is real and inverted, with a negative magnification.
- For a concave mirror, when the object is farther from the mirror than the focal point, the image is real, inverted, and diminished (negative magnification). This corresponds to a negative image distance and a negative magnification, which leads to an inverted image.
Why other options are incorrect:
- A) Concave and convex mirrors can both create inverted images, but a convex mirror always forms virtual, upright images.
- B) A convex mirror always forms upright, virtual images, so it cannot produce a negative magnification.
- C) Convex mirrors cannot form inverted images, they always form upright, virtual images.
- E) Both concave and convex mirrors can form upright images, but a negative magnification specifically correlates with an inverted image, which only happens with concave mirrors for real image formations.
Thus, option D correctly explains that the image is inverted and produced by a concave mirror when the magnification is negative.