Question

A farsighted woman breaks her current eyeglasses and is using an old pair whose refractive power is 1.785 diopters. Since these eyeglasses do not completely correct her vision, she must hold a newspaper 42.00 cm from her eyes in order to read it. She wears the eyeglasses 2.00 cm from her eyes. How far is her near point from her eyes?

Answer 1

The eyeglasses form a virtual image of the newspaper page at her near point.
The image distance is negative, and we can calculate it by using the thin-lens equation. In doing so, we need to keep two things in mind. First, we must take into account the fact that she wear her eyeglasses 2.00 cm from her eyes. This is because the distances that appear in the thin-lens equation are measured with respect to the lens of the eyeglasses, not with respect to her eyes. Thus, the object distance (the location of the newspaper page) is do = 42.00 cm ? 2.00 cm. Second, in using the thin-lens equation we must have a value forthe focal length f, and this is not directly given. However, we do know the refractive power
of the lens, which is the reciprocal of the focal length, according to Equation 26.8. After
calculating the image distance, we can obtain her near point with respect to the eyeglasses by taking the magnitude of this negative number. Finally, we will account for the fact that the Eyeglasses are 2.00 cm from her eyes.