Answer
a. -1.2D.
b. 35 cm.
Work Step by Step
a. The contact lenses are designed to take an object at infinity and make a virtual image 85 cm away from the eye that the person can focus upon. The image is virtual, so the image distance is negative.
$$P=\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{\infty}+\frac{1}{-0.85m}=-1.176D\approx-1.2D$$
b. Now we calculate the near point with the lens in place. Find the object distance that forms a virtual image that is 25 cm in front of the eye.
$$P=\frac{1}{f}=\frac{1}{d_o}+\frac{1}{d_i}$$
$$d_o=\frac{d_i}{Pd_i-1}=\frac{-0.25m}{(-1.176D)(-0.25m)-1}=0.454m=35cm$$
