what is the focal length of a convex lens that forms a magnification of 0.80 if an object is 24.0cm behind the lens?
To find the focal length of a convex lens, you can use the lens formula:
1/f = 1/v - 1/u
Where:
f is the focal length of the lens.
v is the image distance.
u is the object distance.
In this case, the magnification is given as -0.80, which means the image is formed on the same side as the object and is inverted.
Given:
Magnification (m) = -0.80
Object distance (u) = -24.0 cm
Image distance (v) = ? (to be found)
Since the image formed is on the same side as the object, the image distance (v) will also be negative in value.
First, calculate the focal length using the given formula.
1/f = 1/v - 1/u
1/f = 1/(-24.0) - 1/(-24.0) (since u = v = -24.0)
1/f = -2/(-24.0)
1/f = 1/12.0
Now, invert both sides of the equation to find f:
f = 12.0 cm
Therefore, the focal length of the convex lens is 12.0 cm.