Modern microscopes are more likely to use a camera than human viewing. This is accomplished by replacing the eyepiece in Figure 35.14 with a photo-ocular that focuses the image of the objective to a real image on the sensor of a digital camera. A typical sensor is 22.5 mm wide and consists of 5625 4.0@mm@ wide pixels. Suppose a microscopist pairs a 40* objective with a 2.5* photo-ocular.
a. What is the field of view? That is, what width on the microscope stage, in mm, fills the sensor?
b. The photo of a cell is 120 pixels in diameter. What is the cell’s actual diameter, in mm?
That is, what width on the microscope stage, in mm
The photo of a cell is 120 pixels in diameter.
The resolution of a digital camera is limited by two factors:
diffraction by the lens, a limit of any optical system, and the fact
that the sensor is divided into discrete pixels. Consider a typical
point-and-shoot camera that has a 20-mm-focal-length lens and
a sensor with 2.5@mm@wide pixels.
a. First,ass ume an ideal, diffractionless lens. At a distance of
100 m, what is the smallest distance, in cm, between two
point sources of light that the camera can barely resolve? In
answering this question, consider what has to happen on the
sensor to show two image points rather than one. You can use
s′ = f because s W f.
b. You can achieve the pixel-limited resolution of part a only if
the diffraction width of each image point is no greater than
1 pixel in diameter. For what lens diameter is the minimum
spot size equal to the width of a pixel? Use 600 nm for the
wavelength of light.
c. What is the f-number of the lens for the diameter you found in
part b? Your answer is a quite realistic value of the f-number
at which a camera transitions from being pixel limited to
being diffraction limited. For f-numbers smaller than this
(larger-diameter apertures), the resolution is limited by the
pixel size and does not change as you change the aperture. For
f-numbers larger than this (smaller-diameter apertures), the
resolution is limited by diffraction, and it gets worse as you
“stop down” to smaller apertures
A common optical instrument in a laser laboratory is a beam expander. One type of beam expander is shown in FIGURE P35.29.
The parallel ray of a laser beam of width enter from the left.
a. For what lens spacing d does a parallel laser beam exit from the right?
b. What is the width of the exiting laser beam?
Alpha Centauri, the nearest star to our solar system is light years away. assume that alpha centauri has a planet with an advanced civilization. professor Dhg, at the planet's Astronomical Institute, wants to build a telescope with which he can find out whether any planets are orbiting our sun.
(a). What is the minimum diameter for an objectives lens that will just barely resolve Jupiter and the sun? The radius of Jupiter's orbit is Assume
(b). Building a telescope of the necessary size does not appear to be a major problem. What practical difficulties might prevent professor Dhg's experiment from succeeding?
FIGURE shows a simple zoom lens in which the magnitudes of both focal lengths are . If the spacing , the image of the converging lens falls on the right side of the diverging lens. Our procedure of letting the image of the first lens act as the object of the second lens will continue to work in this case if we use a negative object distance for the second lens. This is called a virtual object. Consider an object very far to the left of the converging lens. Define the effective focal length as the distance from the midpoint between the lenses to the final image.
a. Show that the effective focal length is
b. What is the zoom for a lens that can be adjusted from to ?
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