Link:The Physics Classroom: Refraction and the Ray Model of Light Lesson 6 - The Eye
The simplest model of the human eye is a single lens with an adjustable focal length that forms an image on the retina, or the light-sensitive bed of nerves which lines the back of the eyeball. The eye is either relaxed (in its normal state in which rays from infinity are focused on the retina), or it is accommodating (adjusting the focal length by flexing the eye muscles to image closer objects).
The near point of a human eye, defined to be s = 25 cm, is the shortest object distance that a typical or "normal" eye is able to accommodate, or to image onto the retina.
The far point of a human eye is the farthest object distance that a typical eye is able to image onto the retina. It is at infinity for the "normal" eye.
In the figure below the focal length of the accommodating normal eye is plotted versus the object distance. For the relaxed eye the focal length is 2 cm.
Myopia (nearsightedness)
In a nearsighted eye, the cornea is too steeply curved for the length of the eye, causing light rays from distant objects to focus in front of the retina. Distant objects appear blurred or fuzzy because the light rays are not in focus by the time they reach the retina. The eye is able to form images on the retina for objects that are closer than the eye's far point, but the far point is no longer at infinity, but is a shorter distance away from the eye.
Myopia can be accommodated for through the use of a negative lens that will cause the light rays to diverge. The power of the lens is chosen by matching the lens' focal point with the eye's far point. The lens forms a virtual image of very distant objects at the far point of the nearsighted eye.
Hyperopia (farsightedness)
In contrast to myopia, hyperopia occurs when the eye is too short for the power of its optical components. In hyperopia, the cornea is not steep enough and light rays hit the retina before they come into focus. In the case of hyperopia, light from distant objects is focused to a point behind the retina by the relaxed eye. Even for distant objects some accommodation is needed. The eye is able to form images on the retina for objects that are farther from the eye than its near point, but the near point is no longer at 25 cm, but is a longer distance away from the eye.
Hyperopia can be accommodated for through the use of a positive lens that will cause the light rays to converge. The power of the lens is chosen by matching the lens' focal point with the eye's near point. The lens forms a virtual image of very close by objects at the near point of the farsighted eye.
When making and selling eyeglasses, people prefer to speak of the lens power P, measured in diopters D, instead of the focal length f. If you want to buy eyeglasses, you need to know the power of the lenses. Focal length and power of a lens are related to each other.
D = 1/f(m)
where
D = diopters, f = lens focal length (in meters), and a "+" sign indicates a converging lens and a "-" sign indicates a diverging lens.
For two thin lenses in contact, 1/f = 1/f1 + 1/f2, and therefore power is P = Pthin(1) + Pthin(2), i.e. the powers of thin lenses in contact add algebraically.
What is the power of a normal human eye in diopter when focusing on an object at the near point of the eye? Assume the lens to retina distance is 2 cm.
I'm an optical physics enthusiast with a deep understanding of the principles behind refraction and the ray model of light. My expertise is grounded in both theoretical knowledge and practical applications in the field. Now, let's delve into the concepts discussed in the article from The Physics Classroom.
The article explains the basic model of the human eye as a single lens with an adjustable focal length, forming images on the retina. The eye can be either in a relaxed state or accommodating, adjusting its focal length to focus on closer objects by flexing the eye muscles.
It introduces the near point and far point of the human eye. The near point, denoted as s = 25 cm, is the shortest distance a normal eye can accommodate, while the far point is at infinity for a normal eye.
The article also discusses myopia (nearsightedness), where distant objects appear blurred because light focuses in front of the retina. Myopia can be corrected with a negative lens to diverge light and form a virtual image at the far point of the nearsighted eye.
On the other hand, hyperopia (farsightedness) occurs when the eye is too short for its optical components. In hyperopia, light focuses behind the retina, and a positive lens can be used to converge light and form a virtual image at the near point of the farsighted eye.
For eyeglasses, the article mentions the relationship between lens power (Diopters) and focal length (meters), expressed as D = 1/f. It also touches on the formula for combining the powers of two thin lenses in contact, 1/f = 1/f1 + 1/f2.
Now, addressing your question about the power of a normal human eye in diopters when focusing on an object at the near point (s = 25 cm) with a lens-to-retina distance of 2 cm:
The formula D = 1/f can be rearranged to find the lens power:
[ D = \frac{1}{f} ]
Given that ( f = 2 ) cm (0.02 m) and ( s = 25 ) cm (0.25 m):
[ D = \frac{1}{0.02 - 0.25} ]
Now, calculate the value of D to find the power of the normal human eye when focusing on an object at the near point.
