An object is in front of a converging lens (f = 0.36 m). The magnification of the lens is m = 4.8. (a) Relative to the lens, in what direction should the object be moved so that the magnification changes to m = –4.8?
To determine the direction in which the object should be moved so that the magnification changes from 4.8 to -4.8, we need to understand how the magnification of a lens is related to the position of the object.
The magnification (m) of a lens is given by the formula:
m = - v/u
where:
m = magnification
v = image distance from the lens
u = object distance from the lens
For a converging lens, the image formed is real and inverted when the object is placed beyond the focal point (f). In this case, both u and v will be positive.
Since the given lens has a focal length (f) of 0.36 m, we need to determine the initial object distance (u) to find the initial image distance (v).
Given:
f = 0.36 m
m = 4.8
Using the magnification formula:
4.8 = - v/u
Rearranging the formula, we have:
v = -4.8u
Now, to determine the initial object distance (u), we use the formula for the focal length of a converging lens:
1/f = 1/v - 1/u
Plugging in the given values:
1/0.36 = 1/(-4.8u) - 1/u
Simplifying the equation:
2.77 = -1/4.8u
To solve for u, we can cross-multiply:
2.77 * (-4.8u) = 1
This gives us:
-0.9984u = 1
Dividing both sides by -0.9984:
u ≈ -1.0016 m
Since u is negative, it indicates that the object is located to the left of the lens (in relation to the lens).
To change the magnification from 4.8 to -4.8, we need to move the object distance from approximately -1.0016 m to a new position. Increasing the object distance while keeping it negative allows us to move the object to the left, relative to the lens.
Therefore, to achieve a magnification of -4.8, the object should be moved further to the left (in the same direction) in relation to the converging lens.