The near point of a patient's eye is 50.0 cm. What power (in diopters) must a corrective lens have to enable the eye to see clearly an object 25.0 cm away?
Explanation
The patient cannot see clearly an object closer than 50 cm
Therefore, the patient needs a lens that would enable him see clearly, objects placed 25 cm from the lens
So, we take the object to a distance of 25 cm from the lens so that the image forms at 50 cm in front of the lens
u=25cm ;v=-50cm (virtual image); p=
\(\frac{1}{f}\)=\(\frac{1}{u}\) + \(\frac{1}{v}\)
⇒\(\frac{1}{f}\) =\(\frac{1}{50}\)
⇒\(\frac{1}{f}\) = \(\frac{1}{25}\)-\(\frac{1}{50}\)
⇒\(\frac{1}{f}\) = f = 50cm =0.5m
⇒\(\frac{1}{f}\) = \(\frac{2-1}{50}\)
p = \(\frac{1}{f}\)
p = \(\frac{1}{0.5}\)
p = 2 diopters
; The patient needs a converging lens with a power of 2 diopters