Answer:
We have do = 25cm and di = -55cm
So 1/f = 1/do + 1/di = 1/25 + 1/(-55) = 2.214x10^-2
So f = 1/2.214x10^-2 = 45.2cm
So power = 1/0.452m = +2.21 Diopters (converging lens)
The strength lens to be prescribed to correct this vision problem is 2.18 diopters.
From the given information;
Using the Lens formula, we have:
[tex]\mathbf{\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v} }[/tex]
where
For a farsighted person with a near point (v) = 55 cm rather than the normal object distance of u = 25 cm.
Then, The focal length can be determined as follow:
[tex]\mathbf{\dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v} }[/tex]
since the image must be on the same side of the lens, then the image distance must be negative.
∴
[tex]\mathbf{\dfrac{1}{f} = \dfrac{1}{25} + \dfrac{1}{-55} }[/tex]
[tex]\mathbf{\dfrac{1}{f} =0.0218 cm }[/tex]
[tex]\mathbf{f = \dfrac{1}{0.0218 \ cm } }[/tex]
f = 45.8 cm
f = 0.458m
Recall that:
The dioptic power is inverse of the focal length strength;
∴
[tex]\mathbf{D = \dfrac{1}{f}}[/tex]
[tex]\mathbf{D = \dfrac{1}{0.458 }}[/tex]
D = 2.18 diopters.
Learn more about the lens here:
https://brainly.com/question/3225974?referrer=searchResults
