distinction between real and virtual images (Section 23.6)
magnification (Section 23.8)
refraction (Section 23.3)
thin lenses (Section 23.9)
finding images with ray diagrams (Section 23.6)
small-angle approximations (Appendix A.7)
Mastering the Concepts
In a series of lenses, the image formed by one lens becomes the object for the next lens.
If one lens produces a real image that would have formed past a second lens—so that the rays are converging to a point past the second lens—that image becomes a virtual object for the second lens. In the thin lens equation, p is negative for a virtual object.
When the image formed by one lens serves as the object for a second lens a distance s away, the object distance p2 for the second lens is
A typical camera has a single converging lens. To focus on an object, the distance between the lens and the film (or CCD array) is adjusted so that a real image is formed on the film.
The aperture size and the exposure time must be chosen to allow just enough light to expose the film. The depth of field is the range of distances from the plane of sharp focus for which the lens forms an acceptably clear image on the film. Greater depth of field is possible with a smaller aperture.
In the human eye, the cornea and the lens refract light rays to form a real image on the photoreceptor cells in the retina. For most purposes, we can consider the cornea and the lens to act like a single lens with an adjustable focal length. The adjustable shape of the lens allows for accommodation for various object distances, while still forming an image at the fixed image distance determined by the separation of lens and retina. The nearest and farthest object distances that the eye can accommodate are called the near point and far point. A young adult with good vision has a near point at 25 cm or less and a far point at infinity.
The refractive power of a lens is the reciprocal of the focal length:
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663832/24_3.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a> Refractive power is measured in diopters (1 D = 1m–1).
A myopic (nearsighted) eye has a far point less than infinity; for objects past the far point, it forms an image before the retina. A diverging corrective lens (with negative refractive power) can compensate for nearsightedness by bending light rays outward.
A hyperopic (farsighted) eye has too large a near point; the refractive power of the eye is too small. For objects closer than the near point, the eye forms an image past the retina. A converging lens can correct for hyperopia by bending the rays inward so they converge sooner.
As a person ages, the lens of the eye becomes less flexible and the eye's ability to accommodate decreases, a phenomenon known as presbyopia.
Angular magnification is the ratio of the angular size using the instrument to the angular size as viewed by the unaided eye.
The simple magnifier is a converging lens placed so that the object distance is less than the focal length. The virtual image formed is enlarged and upright. If the image is formed at infinity for ease of viewing, the angular magnification M is
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663832/24_6.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (3.0K)</a>
where N, the near point, is usually taken to be 25 cm.
The compound microscope consists of two converging lenses. A small object to be viewed is placed just beyond the focal point of the objective, which forms an enlarged real image. The eyepiece (ocular) acts as a simple magnifier to view the image formed by the objective. If the final image is at infinity, the angular magnification due to the microscope is
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663832/24_8.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (4.0K)</a>
where N is the near point (usually 25 cm) and L (the tube length) is the distance between the focal points of the two lenses.
An astronomical refracting telescope uses two converging lenses. As in the microscope, the objective forms a real image and the eyepiece functions as a magnifier for viewing the real image. The angular magnification is
