Final answer:
The angular magnification is approximately 3.857 times when the diamond is held at 5.68 cm from the magnifying glass with a focal length of 7.70 cm, assuming it is directly in front of the jeweler's eyes and the near-point distance is 22.0 cm.
Step-by-step explanation:
Finding the Angular Magnification
To determine the angular magnification when a jeweler uses a magnifying glass, we can use the lens equation and the magnification equation. Given that the near-point distance of the jeweler is 22.0 cm, and the focal length of the magnifying glass is 7.70 cm, the angular magnification can be found when the diamond is at a distance of 5.68 cm from the magnifying glass.
Angular magnification (m) is given by
m = 1 + (D/f),
where D is the near-point distance and f is the focal length of the lens.
Substituting the given values:
m = 1 + (22.0 cm / 7.70 cm) = 1 + 2.857 = 3.857.
So, the angular magnification is approximately 3.857 times when the diamond is held 5.68 cm from the magnifying glass, assuming the lens is held directly in front of the jeweler's eyes.