Note 11 The Eye The eye is an optical instrument. Optical instrument have primarily three parts to them. There is a part that interacts with the light to form a usable image. There is a part that collects the light. There is the part that interprets or analyze the image.

How Does the Eye Work? The is made of a variable converging . It shapes the light from the outside into an image that falls onto the retina. The retina is a group of cells that convert the light signal into an electrical signals that is then sent to the brain through the optic nerve.

retina lens optic nerve

The lens is adjustable but it has a range of focal lengths. The closest distance you can focus is the near point. The farthest you can focus is the far point. The focal lengths for these two points depend on the size of the eye ball or distance from the lens to the retina. The ideal focusable range of the eye are bound by the two points called the ideal near point and the ideal far point. These are decided to be 25 cm and infinity, respectively. ideal far point focus ideal far point at infinity

ideal near point focus ideal near point at 25 cm

To find the actual focal length, we need the size of the eye ball.

page 1 Sightedness Near-sightedness and far-sightedness are terms that refer to the focusable range of a person’s eye. For near-sightedness, the natural focal length range of the lens is too short. The light is bent too much. There are still near and far points, but they are both closer than ideal. near-sighted near-sighted near point near point focus

ideal far point ideal near point

near-sighted near-sighted far point far point focus

ideal far point ideal near point

near-sighted focal range For far-sightedness, the natural focal length range of the lens is too long. The light is not bent enough. There are still near and far points, but the near point is farther than ideal. far-sighted far-sighted near point near point focus

ideal far point ideal near point

far-sighted far-sighted far point far point focus

ideal far point ideal near point

far-sighted focal range

page 2 Corrective Optics To correct for near-sightedness, we want to increase the effective focal length of the optical system (the corrective optics and the lens of the eye). That is, we need to bend the light less. To bend the light less, we use the diverging lens. Here, an object at the ideal far point is too far. The diverging lens brings it closer to the individual’s far point. near-sighted near-sighted far point far point focus

ideal far point

1 diverging 2 eye object 1 image 1 lens lens at too far to see at far point

object 2 image 2 at far point focused To correct for far-sightedness, we want to decrease the effective focal length of the optical system. To bend the light more, we use the convergent lens. Here, an object at the ideal near point is too close. The converging lens brings it farther to the individual’s near point. far-sighted far-sighted near point near point focus

ideal near point

1 converging 2 eye image 1 object 1 lens lens at too close at near point to see image 2 focused

object 2 at near point

page 3 Optometrists use a shorthand for the focal length of the by defining the reciprocal of the focal length (in meters) as the optical power in a unit called the diopter. This value is found through experimentation rather than calculation because the distance from the lens to the glasses and the size of the eye ball are variables that can’t be calculated. The optical power P is this. 1 P (in dipoters) = f (in meters) Also, the that are made are not double concave or double convex. double convex double concave convex-concave convex-concave

converging lens diverging lens converging lens diverging lens According to the lensmaker equation, 1 ⎛ 1 1 ⎞ = ⎜ − ⎟ n − 1 ⎜ ⎟( lens ) f ⎝R1 R2 ⎠

For the convex-concave converging lens, R1 is positive and R2 is also positive. Furthermore, R2 > R1. This means the focal length is positive thus it is a converging lens.

For the convex-concave diverging lens, R1 is positive and R2 is also positive. Furthermore, R1 > R2. This means the focal length is negative thus it is a diverging lens. If you are near-sighted, your glasses are thicker on the edge than in the middle. If you are far- sighted, you glasses are thicker in the middle than on the edge.

page 4 Example: Far-Sighted Optics A person has a range of distances that he can see clearly from 220 cm to infinity. A corrective lens is placed a distance 2 cm from the lens of the eye. What is the power of the corrective lens?

Solution First, this person is far-sighted. The range of vision is 220 cm to infinity from the eye’s lens. far near eye lens

infinity 220 cm 0 cm The corrective lens we will use here is a converging lens. What the converging lens does is to bring the location of the ideal near-point of 25 cm to the actual near-point of this person’s vision range at 220 cm so that the person can see it clearly. This is what determines the focal length of the converging lens. far near ideal near eye lens

infinity 220 cm 25 cm 0 cm

corrective lens 2 cm We want the corrective lens to do this. 1 1 1 1 1 1 1 1 + = ⇒ + = = = = +3.89 diopters p q f 23 cm −218 cm f 25.7 cm +0.257 m

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