What is the focal length of a contact lens that will allow a person with a near point of 125 cm to read a physics book held 25.0 cm from his eyes?
A)-100 cm
B)-31.3 cm
C)10.2 cm
D)20.8 cm
E)31.3 cm

Question

Quizplus · Accepted Answer

We can use the lens equation:

1/f = 1/d_o + 1/d_i

where f is the focal length of the contact lens, d_o is the distance from the lens to the object (the book) and d_i is the distance from the lens to the image (the retina).

We know that the near point (the closest distance at which the person can focus) is 125 cm, so that means d_i = -125 cm (negative because the image is virtual, on the same side of the lens as the object).

We also know that the person holds the book 25 cm from his eyes, so d_o = 25 cm.

Substituting these values into the lens equation gives:

1/f = 1/25 cm - 1/125 cm

Simplifying:

1/f = (5 - 1)/125 cm = 4/125 cm

f = 31.25 cm

So the focal length of the contact lens that would allow the person to read the book is 31.3 cm, which is closest to choice (E).

What Is the Focal Length of a Contact Lens That