The object distance for a convex lens is 15.0 cm, and the image distance is 5.0 cm. The height of the object is 9.0 cm. What is the height of the image?
To find the height of the image formed by the convex lens, we can use the lens equation:
1/f = 1/do + 1/di
Where:
- f is the focal length of the lens,
- do is the object distance (distance of the object from the lens), and
- di is the image distance (distance of the image from the lens).
However, in this case, we are not given the focal length of the lens. So, we need to find it first.
The magnification formula for a lens is given by:
m = -di / do
Where m is the magnification.
Rearranging this equation, we can write:
di = -m * do
Now, we have all the information we need to find the focal length and the height of the image.
Given that:
do = 15.0 cm (object distance)
di = 5.0 cm (image distance)
m = hi / ho (height of the image / height of the object) =?
From the given data, we know that the height of the object (ho) is 9.0 cm.
Let's start by finding the focal length:
di = -m * do
5.0 cm = -m * 15.0 cm
Solving for m:
m = di / -do
m = 5.0 cm / -15.0 cm
m = -1/3
Now, let's use the magnification formula to find the height of the image (hi):
m = hi / ho
-1/3 = hi / 9.0 cm
Solving for hi:
hi = -1/3 * 9.0 cm
hi = -3.0 cm
Therefore, the height of the image formed by the convex lens is -3.0 cm.