## Step 1: Understanding the Problem A nearsighted person can see objects clearly only up to their far point \( d_o = 4.4 \) m. Glasses are worn at a distance \( d = 2.8 \) cm (or .028 m) from the eye. We need to find the **focal length** (\( f \)) of the glasses so that distant objects (at infinity) are brought into focus at the far point. **Explanation:** The glasses must form an image of a distant object (at infinity) at the person's far point, but measured from the position of the glasses (not the eye). --- ## Step 2: Writing the Expression Use the lens formula for the glasses: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Where: - \( u = \infty \) (object at infinity) - \( v = - (d_o - d) \) (negative because the image is on the same side as the object for a diverging lens; distance from the glasses to the far point) So, \[ \frac{1}{f} = \frac{1}{- (d_o - d)} - \frac{1}{\infty} \] \[ \frac{1}{f} = -\frac{1}{d_o - d} \] \[ f = - (d_o - d) \] **Explanation:** The focal length is negative, indicating a diverging lens, which is required for correcting nearsightedness. --- ## **Final Answer** \[ \boxed{f = - (d_o - d)} \] Where \( d_o \) is the far point of the eye and \( d \) is the distance from the glasses to the eye.