Answer
-27.8 cm.
Work Step by Step
The glasses are designed to take an object at infinity and make a virtual image at the far point of the eye that the person can focus upon.
Use the lens equation and find the image distance for an object at infinity.
$$\frac{1}{f_1}=\frac{1}{d_{o1}}+\frac{1}{d_{i1}}=\frac{1}{\infty}+\frac{1}{ d_{i1}}=\frac{1}{ -26.0cm}$$
$$ d_{i1}=f_1= -26.0cm$$
The virtual image is 26.0 cm in front of the lens, so it is 27.8 cm in front of the eye.
For contact lenses that rest right on the eye, the distance of the image from the contact lens is to be 27.8 cm. The image is virtual, so the image distance is negative.
Use the lens equation and find the focal length. The object is at infinity.
$$\frac{1}{f_2}=\frac{1}{d_{o2}}+\frac{1}{d_{i2}}=\frac{1}{\infty}+\frac{1}{ -27.8cm}$$
$$ f_2=d_{i2}= -27.8cm$$
