# Optical instrument human eye – problems and solutions

1. A normal eye has a far point of infinity. The focal length of the eye lens is 2.5 cm. Determine (a) the image distance (b) lens power.

__Known :__

The focal length of the eye lens (f) = the distance between the cornea and retina = +2.5 cm (The plus sign indicates the converging lens).

The object distance (d_{o}) = infinity

__Wanted__ : the image distance (d_{i})

__Solution :__

**(a) ****the image distance**

1/f = 1/d_{o} + 1/d_{i}

*f = the focal length, d _{o} = the object distance, d_{i} = the image distance*

1/d_{i }= 1/f – 1/d_{o} = 1 / 2.5 – 1 / ~ = 1 / 2.5 – 0

1/d_{i }= 1 / 2.5

d_{i} = 2.5 cm = 0.025 meter

If the object distance is infinity, the image distance (d_{i}) = the focal length (f)

**(b) ****lens power**

P = 1/f = 1/ 0.025 m = 40 Diopters

2. A normal eye has a near point of 25 cm. The image distance is the same as the distance between cornea and retina = 2.5 cm. Determine (a) the focal length (b) lens power

__Known :__

The object distance (d_{o}) = 25 cm

The image distance (d_{i}) = 2.5 cm

__Solution :__

**(a) the focal length (f)**

1/f = 1/d_{o} + 1/d_{i}

1/f = 1/ 25 + 1/ 2,5 = 1/25 + 10/25 = 11/25

f = 2.27 cm = 0.0227 m

The plus sign indicates the converging lens.

**(b) ****lens power (P)**

P = 1/f = 1/ 0.0227 = 44 Diopters

3. One of the optical instrument is human eyes. Determine the properties of image produced by human eyes…

A. Real, upright

B. Real, inverted

C. Virtual, upright

D. Virtual, inverted

Solution

The near point of the normal eye is 25 cm. The near point is the point nearest the eye at which an object is accurately focused on the retina at the full accommodation. The diameter of the human eye is smaller than 25 cm so the focal length of the lens of the eye is also smaller than 25 cm. Thus, the distance of the object (d) must be greater than the focal length of the lens of the eye (f).

The eye lens is a convex lens. Therefore the image formed by the eye lens has the same properties as the image formed by a convex lens. The properties of an image formed by the eye lens when the object distance (s) is greater than the focal length (f) :

real, inverted, smaller

The image should be focused at the retina because the retina converts the light waves into electrical signals transmitted to the brain. Although the image is inverted the human brain turns it upright so that the objects seen by the eye are upright.

When you see a tree from a distance, the tree looks smaller than its actual size. This is in accordance with the properties of the image that is reduced.

The correct answer is A.

4. The eye can see an object when the image is focused on the retina where the properties of the image are…

A. Virtual, upright, greater

B. Virtual, inverted, smaller

C. Real, inverted, smaller

D. Real, upright, smaller

Solution

– The lens of the eye is a convex lens, therefore, the properties of an image formed by the eye lens are similar to the properties of an image formed by the convex lens.

– The near point of the normal eye or the closest distance that can still be seen clearly by the eyes is 25 cm. The eyeballs are so small so the radius of curvature and the focal length of the eye lens is smaller than 25 cm. So can be concluded that the object distance is greater than the focal length.

– If the object distance is larger than the focal length then the properties of an image formed by the human eye at the retina are real, inverted, and smaller. Although the image is inverted, the brain turns it upright as we experience it.

The correct answer is C.

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