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

Question

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

Answer 1

Here's how to solve this problem using the lens equation and magnification formula:**Understanding the Problem**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.**Variables:*** *f*: focal length = +10.0 cm (positive for a convex lens)* *ho*: object height (unknown, but not needed)* *hi*: image height = 3 * ho* *do*: object distance (what we want to find)* *di*: image distance (will be negative since the image is virtual)* *M*: magnification = +3 (positive since the image is upright)**Formulas:*** **Magnification:** M = -di / do = hi / ho* **Lens Equation:** 1/f = 1/do + 1/di**Solution:**1. **Relate image and object distances using magnification:** Since M = 3 and M = -di / do, we have 3 = -di / do, which means di = -3do.2. **Substitute into the lens equation:** 1/10 = 1/do + 1/(-3do)3. **Simplify and solve for do:** 1/10 = (3 - 1) / (3do) 1/10 = 2 / (3do) 3do = 20 do = 20/3 cm ≈ 6.67 cm**Answer:**B. 6.67 cm

Question

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

Solution

Answer