A drop of water on a countertop reflects light from a flower held 2.8 cm directly above it. The flower's diameter is 1.7 cm, and the diameter of the flower's image is 0.17 cm. What is the focal length of the water drop, assuming that it may be treated as a convex spherical mirror?
To find the focal length of the water drop when treated as a convex spherical mirror, we can use the mirror formula:
1/f = 1/di + 1/do
Where:
f is the focal length of the mirror (water drop)
di is the image distance, which is the distance between the image formed by the mirror and the mirror itself
do is the object distance, which is the distance between the object and the mirror itself
First, let's calculate the object distance (do). We know that the flower is held 2.8 cm directly above the water drop. Since the water drop is treated as a mirror, the object distance is the distance between the flower and the mirror, which is 2.8 cm.
Next, let's calculate the image distance (di). We are given that the diameter of the flower's image is 0.17 cm. Since the image is formed by the mirror (water drop), the image distance is the distance between the mirror and the image, which is half the diameter of the image. Therefore, di = 0.17 cm / 2 = 0.085 cm.
Now, we can substitute the values of di and do into the mirror formula:
1/f = 1/di + 1/do
1/f = 1/0.085 + 1/2.8
Simplifying further:
1/f = 11.7647 + 0.3571
1/f = 12.1218
f = 1/12.1218
f ≈ 0.0825 cm
Therefore, the focal length of the water drop (when treated as a convex spherical mirror) is approximately 0.0825 cm.