Answer:
di = 13.5 cm
Virtual image and upright
Step-by-step explanation:
We can use the thin lens equation to determine the location of the image formed by a thin convex lens:
1/f = 1/do + 1/di
where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens.
Substituting the given values, we get:
1/9 = 1/27 + 1/di
Simplifying and solving for di, we get:
1/di = 1/9 - 1/27 = 2/27
di = 27/2 = 13.5 cm
Therefore, the image is located 13.5 cm away from the lens.
To determine the type of image formed, we can use the following rules:
If di is positive, the image is real and located on the opposite side of the lens from the object.
If di is negative, the image is virtual and located on the same side of the lens as the object.
If di is greater than do, the image is inverted.
If di is less than do, the image is upright.
Substituting the values we have found, we get:
di - do = 13.5 cm - 27.0 cm = -13.5 cm
Since di is negative, the image is virtual and located on the same side of the lens as the object. Also, since di is less than do, the image is upright.
Therefore, the image formed by the thin convex lens is a virtual and upright image located 13.5 cm away from the lens.