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Answer :
Your friend can hold the magazine at a distance of approximately 28.27 cm from her eyes and still read it clearly while wearing the contact lenses.
To determine how close your friend can hold a magazine and still read it clearly, we can use the lens formula:
[tex]\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \][/tex]
Where:
- f is the focal length of the contact lens (36.6 cm, given in the problem).
- u is the object distance (distance of the magazine from the lens).
- v is the image distance (distance at which the image is formed on the retina, which is the near point in this case, given as 125 cm).
Rearranging the formula to solve for u:
[tex]\[ u = \frac{1}{\frac{1}{f} + \frac{1}{v}} \][/tex]
Substitute the given values:
[tex]\[ u = \frac{1}{\frac{1}{36.6} + \frac{1}{125}} \][/tex]
[tex]\[ u = \frac{1}{0.0273 + 0.008} \][/tex]
[tex]\[ u = \frac{1}{0.0353} \][/tex]
[tex]\[ u \approx 28.27 \text{ cm} \][/tex]
Therefore, your friend can hold the magazine at a distance of approximately 28.27 cm from her eyes and still read it clearly while wearing the contact lenses.
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