A far sighted person cannot see objects that are less than 100cm away. If this person wants to read a book at 25cm, what type and focal length of lens does he need?
- convex, 20cm
- concave, 20cm
-
convex, 33cm
- concave, 33cm
The correct answer is: C
Explanation
Distance of the object u = −25cm (negative because the object is in front of the lens), Maximum distance the person can see clearly, v = −100cm (also negative for the same reason)
Using lense formula, \(\frac{1}{f}\) = \(\frac{1}{v}\) - \(\frac{1}{u}\)
\(\frac{1}{f}\) = \(\frac{1}{-100}\) - \(\frac{1}{-25}\)
\(\frac{1}{f}\) = \(\frac{1}{-100}\) + \(\frac{1}{25}\) = \(\frac{- 1 + 4}{100}\)
\(\frac{1}{f}\) = \(\frac{3}{100}\)
f = \(\frac{100}{3}\) = 33.33cm
Thus, the person needs a convex lens (since it is used to help a far-sighted person) with a focal length of approximately equal to 33.33cm