Question

Background information
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.

Part A
When glasses (or contact lenses) are used to correct nearsightedness, where should the corrective lens form an image of an object located at infinity in order for the eye to form a clear image of that object?

The lens should form the image at the far point.


Correct
PArt B If a nearsighted person has a far point d_f that is 3.50 m from the eye, what is the focal length f₁ the contact lenses that the person would need to see an object at infinity clearly?

f₁ = ? m

Answer 1

Concepts and reason

The concepts used to solve this problem are physics of eyesight correction for nearsightedness and focal length of concave lens.

Nearsightedness is an eyesight problem in which the person cannot focus on the far point objects.

Use the lens formula to find the focal length of the lens.

Fundamentals

The given below figure shows Nearsightedness.

In the case of nearsightedness the eye’s lens bends the rays from a distant object too much and the rays are brought to a focus before they reach the retina.

The given below figure shows the correction for nearsightedness using diverging lens.

A diverging lens bends the ray outwards before they reach the eye’s lens and the rays are brought to a focus on the retina.

Nearsightedness can be resolved by using concave lens as the corrective lens.

Corrective lenses are the lenses which correct the eyesight artificially.

The lens formula is,

Here, is the focal length of the lens, is the object distance, and is the image distance.

(A)

Nearsightedness can be resolved by using concave lens as the corrective lens.

Concave lenses are thinner in the middle and thicker at the edges.

In a nearsighted eye, the light lands in front of the retina as shown in the figure. Hence in a nearsighted eye, the image is forming in front of the retina

When concave lens used as a corrective lens the clear vision is achieved. Concave lens helps to bend the rays of light outwards and the light converge further and reach the retina.

Hence the concave lens helps to form the image on the retina that means the lens should form the image at the far point.

Therefore, the lens should form the image at the far point.

(B)

The lens formula is,

Here the object distance is infinity. Hence the reciprocal of infinity gives zero.

Substitute for and for

Therefore, the focal length of the contact lenses that the person would need to see an object clearly is .

Ans: Part A

The lens should form the image at the far point.