Solution Found!
Sam purchases +3.50-D eyeglasses which correct his faulty
Chapter 6, Problem 58GP(choose chapter or problem)
Sam purchases +3.50-diopter eyeglasses which correct his faulty vision to put his near point at 25 cm. (Assume he wears the lenses 2.0 cm from his eyes.) Calculate
(a) the focal length of Sam's glasses
(b) Sam's near point without glasses
(c) Pam, who has normal eyes with near point at 25 cm, puts on Sam's glasses. Calculate Pam's near point with Sam's glasses on.
Questions & Answers
QUESTION:
Sam purchases +3.50-diopter eyeglasses which correct his faulty vision to put his near point at 25 cm. (Assume he wears the lenses 2.0 cm from his eyes.) Calculate
(a) the focal length of Sam's glasses
(b) Sam's near point without glasses
(c) Pam, who has normal eyes with near point at 25 cm, puts on Sam's glasses. Calculate Pam's near point with Sam's glasses on.
ANSWER:Step 1 of 3
Consider the provided data as follows.
The power of eyeglasses is \(P = + 3.50{\rm{ diopter}}\).
The faulty vision from the near point is \(25\;{\rm{cm}}\).
The distance between lenses and eyes is \(2.0{\rm{ cm}}\).
Therefore, with lenses, the object distance is:
\(u = 25\;{\rm{cm}} - 2.0\,{\rm{cm}}\)
\( = 23\;{\rm{cm}}\)
(a)
The focal length of Sam’s glass is,
\(f = \frac{1}{P}\)
Substitute the value of \(+ 3.50{\rm{ diopter}}\) for \(P\) in the above equation.
\(f = \frac{1}{{3.50}}\)
\( \approx 0.286\;{\rm{m}}\)
\( = 28.6\;{\rm{cm}} \)
Hence, the focal length of Sam's glasses is \(28.6\;{\rm{cm}} \).