an object that is 6 cm in height is put 9 cm from a convex lens. The lens has a focal length of 8 cm. What is the size of the image?
To find the size of the image formed by a convex lens, we can use the lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance from the lens
u = object distance from the lens
Given:
f = 8 cm
u = 9 cm
We can rearrange the lens formula to solve for v:
1/v = 1/f - 1/u
Substituting the values, we get:
1/v = 1/8 - 1/9
To simplify the equation, we find the common denominator:
1/v = (9 - 8) / (8 * 9)
1/v = 1/72
Now we can solve for v:
v = 72 cm
The negative sign in front of the image distance indicates that the image is formed on the same side as the object, which means it's a virtual image.
Now, to find the size of the image, we can use the magnification formula:
m = -v/u
Given that the object height is 6 cm, we can calculate the image height:
m = -v/u = -72/9 = -8
Since the magnification (m) is negative, it indicates that the image is inverted with respect to the object.
Therefore, the size of the image is 8 times bigger than the object's size, so:
Image height = 8 * 6 cm = 48 cm