Final answer:
The near point of a machinist with normal vision wearing +4.25-diopter eyeglasses is determined by the reciprocal of the lens power. With the eyeglasses, this near point is closer than the normal 25 cm, enabling more precise close-up work.
Step-by-step explanation:
The question posed involves determining the near point of a machinist with normal vision wearing +4.25-diopter eyeglasses. The near point is the closest distance at which the eye can clearly focus on an object. When wearing eyeglasses with a diopter value of +4.25 D, which provide a converging effect, the near point can be brought closer than the normal 25 cm.
To find the new near point, we can use the formula for lens power P (in diopters), which is P = 1/f, where f is the focal length in meters. Rearranging, we get f = 1/P. For +4.25 diopters, the focal length f = 1/4.25 m. Therefore, the near point of the machinist with the eyeglasses can be calculated as the reciprocal of the lens power, giving us a focal length that represents the closest point the machinist can focus on with the eyeglasses.