Final answer:
The maximum angular magnification obtained by an older person with a near point of 45 cm, when using a magnifying glass that provides an angular magnification of 4.5 for a young person with a near point of 18 cm, is 11.25.
Step-by-step explanation:
To calculate the maximum angular magnification obtained by an older person with a near point of 45 cm using a magnifying glass that provides an angular magnification of 4.5 for a young person with a near point of 18 cm, we can use the formula that the angular magnification M is directly proportional to the near point distance. Thus, if we denote the magnification for the young person as Myoung and their near point as Dyoung, and likewise the magnification for the older person as Mold and their near point as Dold, we have the relationship:
Mold = Myoung × (Dold / Dyoung)
Substituting the given values:
Mold = 4.5 × (45cm / 18cm) = 4.5 × 2.5 = 11.25
Therefore, the maximum angular magnification obtained by the older person with a near point of 45 cm is 11.25.