To determine the type of image formed by a lens, we need to consider two key aspects: the magnification factor [tex]\( m \)[/tex] and its sign.
1. Magnification [tex]\( m \)[/tex]:
- If [tex]\(|m| > 1\)[/tex], the image is larger than the object.
- If [tex]\(|m| < 1\)[/tex], the image is smaller than the object.
2. Sign of Magnification:
- A positive magnification ([tex]\( m > 0 \)[/tex]) indicates that the image is upright and virtual.
- A negative magnification ([tex]\( m < 0 \)[/tex]) indicates that the image is inverted and real.
Given:
- [tex]\( m = -0.87 \)[/tex]
Let's analyze this:
1. Size of the Image:
- The absolute value of [tex]\( m \)[/tex] is [tex]\( |m| = 0.87 \)[/tex].
- Since [tex]\( 0.87 < 1 \)[/tex], the image is smaller than the object.
2. Nature of the Image:
- [tex]\( m \)[/tex] is negative ([tex]\( m = -0.87 \)[/tex]), indicating that the image is inverted.
- An inverted image formed by a lens is a real image.
Hence, combining these observations, we can conclude that:
- The image formed is smaller than the object.
- The image is real.
Therefore, the correct answer is:
A. The image is smaller than the object and is real.
