When a person with a near point at 28 cm uses a certain magnifying glass, it produces an angular magnification of 7.0 with the image very distant. What is the focal length of the lens of this
Magnifying glass?
A) $6.0 \mathrm {~cm}$
B) $5.0 \mathrm {~cm}$
C) $2.0 \mathrm {~cm}$
D) $3.0 \mathrm {~cm}$
E) $4.0 \mathrm {~cm}$

Question

When a person with a near point at 28 cm uses a certain magnifying glass, it produces an angular magnification of 7.0 with the image very distant. What is the focal length of the lens of this
Magnifying glass? 
A) $6.0 \mathrm {~cm}$
B) $5.0 \mathrm {~cm}$
C) $2.0 \mathrm {~cm}$
D) $3.0 \mathrm {~cm}$
E) $4.0 \mathrm {~cm}$

Quizplus · Accepted Answer

The angular magnification (M) of a magnifying glass when the image is at infinity is given by $M = 1 + \frac{D}{f}$, where $D$ is the near point distance (in meters) and $f$ is the focal length of the lens (also in meters). Given $M = 7.0$ and $D = 28 \, \text{cm} = 0.28 \, \text{m}$, we can solve for $f$: $7 = 1 + \frac{0.28}{f}$, which simplifies to $6 = \frac{0.28}{f}$, giving $f = \frac{0.28}{6} = 0.0467 \, \text{m} = 4.67 \, \text{cm}$, which is closest to $4.0 \, \text{cm}$.

When a Person with a near Point at 28 Cm 6.0 cm6.0 \mathrm {~cm}6.0 cm

When a Person with a near Point at 28 Cm $6.0 \mathrm {~cm}$