Question

A person with normal vision can focus on objects as close as a few centimeters from the eye up to objects infinitely far away. There exist, however, certain conditions under which the range of vision is not so extended. For example, a nearsighted person cannot focus on objects farther than a certain point (the far point), while a farsighted person cannot focus on objects closer than a certain point (the near point). Note that even though the presence of a near point is common to everyone, a farsighted person has a near point that is much farther from the eye than the near point of a person with normal vision.

Both nearsightedness and farsightedness can be corrected with the use of glasses or contact lenses. In this case, the eye converges the light coming from the image formed by the corrective lens rather than from the object itself.

Required:
a. If a nearsighted person has a far point df that is 3.50 m from the eye, what is the focal length f1 of the contact lenses that the person would need to see an object at infinity clearly?
b. If a farsighted person has a near point that is 0.600 m from the eye, what is the focal length f2 of the contact lenses that the person would need to be able to read a book held at 0.350 m from the person's eyes?

Answer 1

a) f₁ = 3.50 m , b) f₂ = 0.84 m

Step-by-step explanation:

For this exercise we must use the constructor equation

1 / f = 1 / p + 1 / q

where f is the focal length, p is the distance to the object and q is the distance to the image

a) the distance where the image should be placed is q = 3.50 m and the object is located at infinity p = ∞

1 / f₁ = 1 /∞ + 1 / 3.50

f₁ = 3.50 m

b) in this case the image is at q = -0.600 m and the object p = 0.350 m

1 / f₂ = 1 / 0.350 -1 / 0.600

the negative sign, is because the image is in front of the object

1 / f₂ = 1,1905

f₂ = 1 / 1,1905

f₂ = 0.84 m