Final answer:
The magnification and image distance for a 14 D magnifier can be calculated using the formulae for angular magnification and lens optics, with the focal length derived from the lens power and image distance set to the typical near point.
Step-by-step explanation:
The task is to calculate the magnification and image distance using a magnifier with a power specified. The typical near point is given as 25 cm, and the distance from the lens to the retina is 1.7 cm. The magnifier has a power of 14 D, and the angular magnification (M) can be calculated as M = 1 + (0.25 m / f), where f is the focal length in meters. The focal length (f) can be determined from the power (P) using the formula P = 1/f. The image distance (L) for maximum magnification can be calculated by setting L = 25 cm and 1 = 0 cm, as per the reference equations provided.
To begin the calculation step, convert the power into focal length: Power (P) in diopters = 1 / focal length (f) in meters, so f = 1 / P. As P = 14 D, f = 1/14. To find the image distance, we use the lens formula 1/f = 1/o + 1/i, where o is the object distance and i is the image distance. Since we're placing the image at the near point, we want it to be at 25 cm, hence i = L = 25 cm, providing the maximum magnification attainable without eyestrain.