Images by Refraction Thin Lenses Locating Images Now
Images by Refraction Thin Lenses: Locating Images
Now that we’ve studies how images form through reflection, lets examine how refraction processes can also lead to the formation of images. What happens to light when it enters a piece of glass from air?
As was the case for spherical mirrors, a spherical piece of glass also has a center of curvature. n 2 It turns out (using geometry and Snell’s Law) that: n 1 object image p is the distance of the object from the surface q is the distance of the image from the surface
Unlike the mirror, however, for refracting surfaces, we use the following sign conventions: p > 0 if the object is in front of the surface (real) p < 0 if the object is in back of the surface (virtual) q > 0 if the image is in back of the surface (real) q < 0 if the image is in front of the surface (virtual) R > 0 if center of curvature is in back of the surface (a convex surface). R < 0 if the center of curvature is in front of the surface (concave mirror).
The magnification provided by the refracting surface is given by What happens if the refracting surface is flat? That is, where does the image of a plane refracting surface form? A plane has a radius of curvature equal to infinity, so. . .
So for a plane refracting surfaces, the image formed is always on the same side of the surface as the object. Air n=1. 00 Water n=1. 33 object image
Glass or plastic ground so that each of its two refracting surfaces are either planes or parts of a sphere.
There are two basic types of lenses: Converging Thickest in the middle. Bring light rays from infinity to a focus on the opposite side of the lens. Diverging Thinnest in the middle. Parallel light rays from infinity diverge as they pass through the lens.
Light can pass through a lens in either direction. So it’s not surprising that a lens will have two foci. focal length, f The thin lens equation relates the object and image distances to the focal length.
We need to define yet one more set of sign conventions to make sense of this equation. For lenses. . . p > 0 if the object is in front of the lens (real) p < 0 if the object is in back of the lens (virtual) q > 0 if the image is in back of the lens (real) q < 0 if the image is in front of the lens (virtual) f > 0 for a converging lens. f < 0 for a diverging lens.
Each surface of a thin lens has its own radius of curvature (R 1 and R 2) t n o k c a fr R 2 b R 1 and R 2 > 0 if the center of curvature is on the back side of the lens. R 1 and R 2 < 0 if the center of curvature is on the front side of the lens.
The focal length of the lens (in air) is related to the radii of curvature of the lens surfaces and the index of refraction of the material out of which the lens is made. Where R 1 is the radius of curvature of the front surface of the lens and R 2 is the radius of curvature of the back of the lens.
t n o fr k c a b The front side of the lens is the side on which light is approaching. The back side of the lens is the far side of the lens.
1) A ray parallel to the principle axis of the lens will be refracted to pass through (or appear to originate from) focal point of the front side of the lens. t on fr “focus of back surface” Converging Lens k c a b “focus of front surface”
What do I mean by “focal point of the front surface? ” After all, lenses have only one focal length (given by the lens maker’s equation). So the distance to the lens of the focal point in front equals the distance to the lens of the focal point in back! Converging Lens “focus of back surface” Diverging Lens “focus of front surface” “focus of back surface”
1) A ray parallel to the principle axis of the lens will be refracted to pass through (or appear to originate from) focal point of the front side of the lens. [Things look a little different for the diverging lens!] t n o fr k c a b “focus of front surface” Diverging Lens “focus of back surface”
2) A ray headed directly toward the center of the lens will approximately pass straight through the lens. [This works for the diverging lens as well. ] t on fr focus Converging Lens k c a b focus
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