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.

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?
b. If a nearsighted person has a far point df 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?

Answer 1

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

Answer:

a. When glasses (or contact lenses) are used to correct nearsightedness, the lens should form the image at the far point.

b. If a nearsighted person has a far point df 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?

f 1 = -3.50 m

Explanation:

a. Nearsightedness (the person cannot focus on the far point objects) physics of eyesight correction,  can be resolved by using focal length of concave lens as the corrective lens, which correct the eyesight artificially, as 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.  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.  

The lens formula to find the focal length of the lens is:

                       1/f = 1u + 1/v

Where, f is the focal length of the lens, u is the object distance, and v  is the image distance.

The light lands in front of the retina, so the image is forming in front of the retina .When concave lens used as a corrective lens the clear vision is achieved, helping to bend the rays of light outwards and the light converge further and reach the retina to form the imagemeaning the lens should form the image at the far point.

b.      The lens formula is,

                        1/f = 1u + 1/v

Here the object distance is infinity,so the reciprocal of infinity gives zero.

    Substitute 0.0  for u   and 0.0 -3.50 m    for   v  

1/f = 1/ -3.50m  + 1/ 0.0

Therefore, the focal length of the contact lenses that the person would need to see an object clearly is -3.50 m