# Eyeglass, farsightedness, nearsightedness

Nearsightedness can be normalized using eyeglass lenses and contact lenses. Eyeglass lenses are affixed to the eyeglass while contact lenses are attached to the eyeball. Eyeglass has a certain distance from the eye while the contact lenses stick to the eye so that the distance between the contact lens and the eye can be ignored.

In this paper, we explain examples of problems experienced by sufferers of nearsightedness and farsightedness, the type of lens used to normalize the eye, and the focal length and the power of the lens. This focuses on the use of glasses to normalize nearsightedness and farsightedness.

**Farsightedness ****and eyeglass**

The farthest distance that can be seen clearly by a person with nearsightedness is 102 cm. Determine (a) the type of lens used, (b) the focal length of the lens, (c) the power of the lens so that the nearsighted eyes can see infinite objects.

Eyeglass lenses are generally 2 cm from the eye.

Solution

(a) __The type of lens used__

On the topic of nearsightedness, it has been explained that the lens used to normalize nearsighted eyes is a concave lens or divergent lens or negative lens.

(b) __The focal length of the lens__

The object that is observed nearsighted eyes through the eyeglass is at infinite, so the lens must form an image at a distance of 102 cm in front of the eye. The eyeglass lens is 2 cm from the eye, so the image is 100 cm in front of the lens. The image is in front of the lens, so the image is virtual and upright (compare the explanation on the topic of the image formation of the concave lens)

__Known:__

The object distance (do) = infinite

The image distance (di) = -100 cm (negative means image is virtual)

__Wanted:__ the focal length (f)

__Solution:__

1/f = 1/do + 1/di

1/f = 1/~ + (- 1/100)

1/f = 0 – 1/100

1/f = – 1/100

f = – 100/1 cm = -100 cm = -1 meter.

The focal length is negative, means that the lens used is a concave lens or a diverging lens.

(c) __Power of lens__

P = 1/f = 1/-1 m = -1 Diopter

The power of the lens is -1 D. Negative sign means the lens used is a concave lens or divergent lens.

**Nearsightedness and eyeglass**

The closest distance that can be seen clearly by a sufferer of nearsightedness is 102 cm. For the person to be able to read at a distance of 25 cm in front of the eyes, determine (a) the type of lens used, (b) the focal length of the lens, (c) the power of the lens. Eyeglass lenses are generally 2 cm from the eye.

Solution

__(a) The type of lens used__

The lens used to normalize nearsighted eyes is a convex lens or convergent lens or positive lens.

__(b) The focal length of the lens__

The object observed is 25 cm in front of the eye so the lens must form an image at a distance of 102 cm in the front of the eye. The eyeglass lens is 2 cm in the front of the eye so the image is 100 cm in the front of the eyeglass lens and the object is 23 cm in the front of the eyeglass lens. The image is in the front of the lens, so the image is upright and virtual

__Known:__

The object distance (do) = 23 cm

The image distance (di) = -100 cm (negative means the image is virtual)

__Wanted:__ the focal length (f)

__Solution:__

1/f = 1/do + 1/di

1/f = 1/23 + 1/-100

1/f = 1/23 – 1/100

1/f = 100/2300 – 23/2300

1/f = 77/2300

f = 2300/77 = 30 cm = 0.3 meters

The focal length signed positive means that the lens used is a convex lens or convergent lens or positive lens.

__(c) Power of lens__

P = 1/f = 1/0.3 = +3 Diopters

The power of the lens is +3 D. Positive sign means that the lens used is a convex lens or convergent lens.