33.8 - Interactive problem: optical bench with a lens
Your mission here is to create the image at the location shown in the graphic at the
right. The image is 13.5 cm tall, and 15.0 cm from the lens. The object is 9.0 cm tall.
(Note: We are deliberately being ambiguous about mathematical signs here!)
You set both the object location and the lens’s focal length to the nearest 0.01 cm in
this simulation. Press CHECK to test your answer.
A hint: Start this problem by determining the magnification required for the specified
image height, and then consider how that helps you to specify the object distance. If
you need help with this problem, consult the section on lens equations. You will
need to apply three equations from that section.
33.9 - The human eye
The human eye contains a variable lens. This organ í a remarkable product of evolution
í employs the lens to focus images on the retina at its back surface. Special cells called
rods and cones line the retina. Light stimulates these cells, and they send signals in the
form of electric impulses to the brain via the optic nerve.
Light passes through four different components of the eye on its way to the retina: the
cornea, the aqueous humor, the lens, and the vitreous humor. Each has a different
index of refraction, ranging from about 1.30 to 1.40. This means the greatest amount of
refraction occurs when the light first crosses from the air (n = 1.00) to the cornea,
where the indices differ the most.
In order for an object to be perceived clearly, its image must be focused on the retina, at
a fixed distance from the lens. The real image projected on the retina is upside down,
but the brain automatically corrects for this.
The eye must be able to create crisp images of objects that are located at varying
distances. It accomplishes this by changing the shape of the lens, a process called
accommodation. By causing the lens to contract or expand, the eye changes the radius
of curvature and the focal length of the lens. On the right, you see the lens in both a
relaxed state for viewing objects far away, and tensed as its curvature has been
changed to focus on a nearer object.
The closest distance at which an object can be brought into focus is called the near
point. A young adult with a fully tensed lens can clearly see objects that in some cases
are as close as 15 cm, with an average near point for this age being 25 cm. By the time
a person reaches her early forties, the near-point distance increases to an average of
40 cm. By age 65, the average near-point distance is 400 cm. Changes in the eye that
occur with aging explain this increase. In fact, this progression is so predictable that the
distance to the near point can pinpoint age to within a few years.
The far point is the greatest distance at which an object can be seen clearly. For people
who do not need glasses for distance vision, this point is effectively infinitely far away.
For those who are nearsighted, it can be much closer.
If you have 20/20 vision, you are lucky: You perceive objects crisply without the use of
prescription lenses. If you have 20/60 vision, it means that you must be as close as 20
feet to see what a person with typical vision can see at 60 feet. Baseball players are
noted for having acute vision, such as 20/15 vision. This means they see at 20 feet
what most people need to be within 15 feet to see clearly.
Human Eye
Contains variable lens
Image forms on retinaNear point
Closest in-focus object distance
Far point
Farthest in-focus object distance