An object 4cm high is placed 25cm from a covering lens of focal length 15cm the image height is
first, find the image distance.
1/do+1/di=1/f
then find the height: M=di/do=Hi/ho
To find the image height, we 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 from the lens (also known as the image distance),
u is the object distance from the lens (also known as the object distance).
Given:
f = 15 cm
u = 25 cm
First, we need to find the image distance (v).
Using the lens formula, we can rearrange it to solve for v:
1/v = 1/f - 1/u
Substituting the given values:
1/v = 1/15 - 1/25
To simplify this equation, we can find the common denominator:
1/v = (25 - 15)/(15*25)
= 10/375
Taking the reciprocal of both sides:
v = 375/10
= 37.5 cm
Now that we know v, we can find the magnification (M) using the formula:
M = -v/u
Substituting the given values:
M = -37.5/25
= -1.5
Note: The negative sign indicates that the image is inverted.
The image height (h') is related to the object height (h) by the magnification:
M = h'/h
Rearranging this equation, we can solve for h':
h' = M * h
Substituting the given values:
h' = -1.5 * 4
= -6 cm
Therefore, the image height is -6 cm (inverted image).