Answer
3.9D.
Work Step by Step
We calculate the 60-year-old man’s near point using the lens equation, with the object distance as 0.38 m, and a 2.5-D lens.
$$P_1=\frac{1}{d_{o1}}+\frac{1}{d_{i1}}$$
$$d_{i1}=\frac{d_{o1}}{P_1d_{o1}-1}=\frac{0.38m}{(2.5D)(0.38m)-1}=-7.6m$$
An object held at 38 cm, with his old reading glasses, places the image at 7.6 m in front of the lens. This must be the 60-year old man’s near point without glasses.
To find the 60-year-old’s new prescription, set the object distance as 0.25 m, and the image distance at -7.6 m. Calculate the necessary lens power to have this happen.
$$P_2=\frac{1}{d_{o2}}+\frac{1}{d_{i2}}$$
$$P_2=\frac{1}{0.25m}+\frac{1}{-7.6m}=+3.9D$$
