Optics - Diopter farsighted + shortsigted

1. Jul 14, 2011

zimo

1. The problem statement, all variables and given/known data
A man is both farsighted and shortsighted so his natural correct view is between 70cm to 100cm.
What will be his view range if he puts on his reading glasses?

2. Relevant equations

$$\frac{1}{u}+\frac{1}{v} = \frac{1}{f} = D$$

3. The attempt at a solution
I calculated diopter for his farsightness and came with D=2.571 (1/0.25 - 1/0.70 = 2.571
Now, I wanted to know what will be the his maximum range and have come to the equation:
$$\frac{1}{u}-\frac{1}{\infty} = 2.571$$
And the solution for u is 38.889cm, so the view range will be between 25cm to 38.889cm.
Now, there is another opinion in our class that when I use the equation to reveal the limit to his view range I should put 1/100cm instead of $$\frac{1}{\infty}$$ because the man can see to 100 cm at max and not to the extent of the horizon.

What is the correct way and why?

Thank you

2. Jul 14, 2011

cupid.callin

the reading lens should have power such that for object at near point of vision (25cm) its image should form at 70cm ... so that eye lens can focus it.
find power of it that way ...
now for far point ... when object is at u ... its image should be at 100cm ... so solve for u (answer)