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Chapter 35: Q.34 (page 1018)
The cornea, a boundary between the air and the aqueous humor, has a focal length when acting alone. What is its radius of curvature?
The radius of curvature is
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The rays leaving the two-component optical system of FIGUREPproduce two distinct images of the-tall object. what are the position (relative to the lens), orientation, and height of each image?
The resolution of a digital cameras 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. consirer a typical point-and--shoot camera that has a lens and a sensor with pixels.
(a) . First, assume an ideal, diffractionless lens, at a distance of what is the smallest distance, in 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
(b) . You can achieve the pixel-limied resolution of part a only if the diffraction which of each image point no greater than the diffraction width of image point is no greater than pixel in diameter. for what lens diameter is the minimum spot size equal to the width of a pixel ? use for the wavelength of light.
(c). what is the of the lens for the diameter you found in part b? your answer is a quite realistic value of the at which a camera transitions from being pixel limited to being diffraction limited for smaller than this (larger-diameter apertures), the resolution is limited by the pixel size and does not change as you change the apertures. for larger than this (smaller-diameter apertures). the resolution is limited by diffraction and it gets worse as you "stop down" to smaller apertures.
A reflection telescope is build with a diameter mirror having a focal length. it is used with a eyepiece. what are
(a) the magnification and
(b) the of the telescope?
Mordern microscopes are more likely to use a camera than human viewing. This is accomplished by replacing the eyepiece in figure with a photo-ocular that focuses the image of the objectives to a real image on the sensor of a digital camera. A typical sensor is wide and consists of wide pixels. suppose a microscopist pairs a objectives with a photo-ocular
a. what is the field of view? That is what width on the microscope stage in fills the sensor?
b. The photo of a cell is in a diameter. what is the cell's actual diameter in?
Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart. If the lens of your eye is diffraction limited, at what distance are the two headlights marginally resolved? Assume a wavelength of 600 nm and that the index of refraction inside the eye is 1.33. (Your eye is not really good enough to resolve headlights at this distance, due both to aberrations in the lens and to the size of the receptors in your retina, but it comes reasonably close.)
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