Final answer:
The magnification produced by a -4.00 D lens when an object is held 25.0 cm away is 0.5. This means the image will be half the size of the object.
Step-by-step explanation:
To calculate the magnification produced by a lens, we can use the lens formula and the magnification formula:
The lens power P is related to the focal length f in meters by the equation P = 1/f. Given a power P of -4.00 D, we first convert the power to the focal length:
f = 1/P = -1/4 = -0.25 m, which is the same as -25.0 cm since 1 m = 100 cm.
The magnification m is given by the formula m = -di/do, where di is the image distance and do is the object distance.
As we have the object distance do = 25.0 cm, we use the lens formula to find di:
1/f = 1/do + 1/di
1/-25 = 1/25 + 1/di
Solving for di gives us di = -12.5 cm (negative sign indicates that the image is formed on the same side of the lens as the object, which is characteristic of diverging lenses like those used to correct myopia).
Now, we calculate the magnification:
m = -di/do = -(-12.5)/25 = 0.5
Therefore, the magnification produced by a -4.00 D lens when an object is held 25.0 cm away is 0.5, which means the image will be half the size of the object.