Introductory Physics Volume Two
Introductory Physics Volume Two
Introductory Physics Volume Two
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166 Geometric Optics 8.6<br />
α<br />
β<br />
β<br />
Show that the net deflection of the beam (2β) is<br />
§ 8.6 Thin Lens Equation<br />
Imagine that we take a stack<br />
of prisms as shown in the diagram.<br />
Since the prisms farther<br />
from the middle have a steeper<br />
angle they bend the light ray<br />
more sharply. If we pick the angle<br />
of each prism correctly all<br />
of the rays will converge on the<br />
same point.<br />
2β = 2 arcsin(n sin α 2 ) − α<br />
Such a device was used in old light houses in order to focus the<br />
light on the horizon (where there are ships that want to see the light)<br />
rather than letting it spread out and go into the water or into the sky.<br />
Now imagine that you make<br />
the prisms in the middle thicker,<br />
without changing the angle of<br />
the faces. We would now end<br />
up with a smooth curved surface.<br />
Since the angle of faces was not<br />
changed the light would still converge<br />
on the single point. You<br />
can see that you get a lens. This<br />
type of lens is called a converging<br />
lens, since it bends the rays<br />
toward each other.<br />
focal length<br />
focal<br />
point<br />
The optical axis of the lens is a line that passes through the center<br />
of the lens, that is normal to the surface of the lens. A focus is a point<br />
where rays converge. The focus of rays that are parallel to the optical<br />
axis is called the principle focus or focal point. The distance between<br />
the lens and the focal point is called the focal length of the lens.<br />
Suppose that you set up your lens at sunrise, so that the rays are<br />
parallel to the optical axis and converge at the focal point. If you come
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