24. At what distance above this computer screen would a convex magnifying lens that has a focal length of 10.0 cm have to be held for the image of the letters to appear upright and 3 times as tall? A. 3.33 cm B. 6.67 cm C. 13.3cm D. 15.0 cm

Here's how to solve this problem using the lens equation and magnification formula:<br /><br />**Understanding the Problem**<br /><br />We want a *upright* and *magnified* image. This means the image must be virtual, and the object (the computer screen) must be located between the lens and its focal point.<br /><br />**Variables:**<br /><br />* *f*: focal length = +10.0 cm (positive for a convex lens)<br />* *h_o*: object height (unknown, but not needed)<br />* *h_i*: image height = 3 * h_o<br />* *d_o*: object distance (what we want to find)<br />* *d_i*: image distance (will be negative since the image is virtual)<br />* *M*: magnification = +3 (positive since the image is upright)<br /><br />**Formulas:**<br /><br />* **Magnification:** M = -d_i / d_o = h_i / h_o<br />* **Lens Equation:** 1/f = 1/d_o + 1/d_i<br /><br />**Solution:**<br /><br />1. **Relate image and object distances using magnification:** Since M = 3 and M = -d_i / d_o, we have 3 = -d_i / d_o, which means d_i = -3d_o.<br /><br />2. **Substitute into the lens equation:**<br /> 1/10 = 1/d_o + 1/(-3d_o)<br /><br />3. **Simplify and solve for d_o:**<br /> 1/10 = (3 - 1) / (3d_o)<br /> 1/10 = 2 / (3d_o)<br /> 3d_o = 20<br /> d_o = 20/3 cm ≈ 6.67 cm<br /><br />**Answer:**<br /><br />B. 6.67 cm<br />