To allow a person with a near point of 73.0 cm to see objects at 25.0 cm, the power of the contact lens required is approximately -5.37 D, calculated using the lens formula and converting the focal length into diopters.
The question relates to finding the power of a contact lens needed to correct a person's vision. To determine the power of a contact lens that allows someone with a near point of 73.0 cm to see objects at 25.0 cm, we can use the lens formula 1/f = 1/do + 1/di, where f is the focal length, do is the object distance (in this case, the near point), and di is the image distance (the distance at which they want to see clearly, 25 cm). The power P of the lens, which is what is needed for the prescription, is given by P= 1/f, where f should be in meters and P in diopters (D). Since the lens will form an image at the person's near point when looking at objects 25 cm away, the image distance will be the negative of the near point distance, as it's a virtual image formed on the same side of the lens as the object.
In this case, do = 25 cm = 0.25 m and di = -73 cm = -0.73 m. Applying the lens formula, we get:
1/f = 1/do - 1/di
1/f = 1/0.25 - 1/-0.73
1/f = 4 - (-1.36986)
1/f = 5.36986
f ≈ 0.1862 m
The power P = 1/f, so P ≈ 1/0.1862 ≈ 5.37 D. However, since contact lenses are typically marked with a negative sign for myopic (nearsighted) correction:
P = -5.37 D