Answer:
P = 4 D
Step-by-step explanation:
To calculate the additional power that a lens must provide in order to focus clearly on an object at the standard near point, we can use the formula:
P = 1/f
where P is the power of the lens in diopters (D) and f is the focal length of the lens in meters (m).
The standard near point is defined as 0.25 m, so the lens must be able to focus at this distance. To calculate the required power of the lens, we need to determine the focal length that corresponds to a distance of 0.25 m.
Using the formula for thin lenses, we can write:
1/f = 1/do + 1/di
where do is the object distance (the distance from the object to the lens) and di is the image distance (the distance from the lens to the image).
Since we want the lens to focus at the standard near point, we can assume that the object distance is infinity (do = ∞). This gives:
1/f = 0 + 1/di
1/f = 1/di
di = f = 0.25 m
So the focal length of the lens required to focus at the standard near point is 0.25 m.
Now we can calculate the additional power that the lens must provide by subtracting the power of a lens with a focal length of infinity (which corresponds to a power of 0 D) from the power of the lens with a focal length of 0.25 m:
P = 1/f - 1/∞
P = 1/0.25 - 1/∞
P = 4 - 0
P = 4 D
Therefore, the lens must provide an additional power of 4 D in order to focus clearly on an object at the standard near point of 0.25 m.