A common optical instrument in a laser laboratory is a beam expander. one type of beam expander is shown in FIGURE P.
a. For what lens spacing d does a parallel laser beam exit from
b. What is the width of the exiting laser beam?
a. Lens spacing d does a parallel laser beam exit from the right .
b. The width of the exiting laser beam is .
We need to find what lens spacing d does a parallel laser beam exit from the right.
We find this distance as the sum of the focal length of the first lens and the focal length of the second lens:
We need to find the width of the exiting laser beam.
let us find width ,
Here, is the width of the first lens, is the width of the second lens, is the focal length of first lens and second lens.
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.)
Two converging lenses with focal lengths of and are apart. A tall object is in front of the focal-length lens.
a. Use ray tracing to find the position and height of the image. Do this accurately using a ruler or paper with a grid, then make measurements on your diagram.
b. Calculate the image position and height. Compare with your ray-tracing answers in part a.
High-power lasers are used to cut and weld materials by focusing the laser beam to a very small spot. This is like using a magnifying lens to focus the sun’s light to a small spot that can burn things. As an engineer, you have designed a laser cutting device in which the material to be cut is placed 5.0 cm behind the lens. You have selected a high-power laser with a wavelength of 1.06 mm. Your calculations indicate that the laser must be focused to a 5.0@mm@diameter spot in order to have sufficient power to make the cut. What is the minimum diameter of the lens you must install?
An astronomer is trying to observe two distant stars. The stars are marginally resolved when she looks at them through a filter that passes green light with a wavelength near 550 nm. Which of the following actions would improve the resolution? Assume that the resolution is not limited by the atmosphere.
A. Changing the filter to a different wavelength. If so, should she use a shorter or a longer wavelength?
B. Using a telescope with an objective lens of the same diameter but a different focal length. If so, should she select a shorter or a longer focal length?
C. Using a telescope with an objective lens of the same focal length but a different diameter. If so, should she select a larger or a smaller diameter?
D. Using an eyepiece with a different magnification. If so, should she select an eyepiece with more or less magnification?
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