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**Properties of Thin Lenses**

Lens Maker’s Equation Ray Tracing Equations

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Although each face of a lens is part of a sphere and these spheres have centers. The actual center of the lens itself is exactly between the centers of each face. r1 r2 C r1 r2 Note the position of C1 and C2 changes depending on whether the lens face is concave or convex.

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**Just like for mirrors the principal axis goes through the center of the lens.**

Unlike a mirror, the principal axis must go through the center of the faces as well. There is, therefore, only one principal axis for a lens. C C

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**Each lens has two focal points.**

There is one focal point on each side. The focal points are the same distance from the center for a thin lens. C F F C F F

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**The shape of the lens determines whether the rays converge or diverge from it.**

The lens maker’s equation will tell us which shapes are which. C F C F

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Each lens has two radii and using these and the refractive index of the lens, we can find the focal length of the lens. Normally, the thickness of the lens must be considered. For a thin lens, we use the lens maker’s equation r is negative for concave faces and positive for convex (as seen from the object). r1 is the radius of curvature of the face closest to the object and r2 is the radius of curvature of the other face. f is positive for converging lenses and negative for diverging lenses.

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Although any ray may be traced to find out where an image point is, there are three principal rays that make the job easier. 1. Parallel Ray: Comes in parallel to the principal axis and goes out through the image focal point. 2. Focal Ray: Comes in through the object focal point and goes out parallel to the principal axis. 3. Radial Ray: Comes in through the center point and continues unchanged. C F

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Although any ray may be traced to find out where an image points is, there are three principal rays that make the job easier. 1. Parallel Ray: Comes in parallel to the principal axis and goes out as though it came from the object focal point. 2. Focal Ray: Comes in toward the image focal point and goes out parallel to the principal axis. 3. Radial Ray: Comes in toward the center point and continues unchanged. C F

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**Negative di Positive di Positive do**

Object distance (do) is positive. Image distance (di) is negative if it is on the same side as the object and positive if it is not. Heights (ho for object and hi for image) are still positive if the image or object is right-side up and negative if they are up-side down. Negative di Positive do Positive di

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**Converging lenses have positive focal length.**

Diverging lenses have negative focal length. Positive f Negative f

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The same equation may be used to find the image distance, object distance or focal length for all thin lenses. This is called the thin lens equation. (Notice its similarity to the mirror equation.) The magnification equation is the same as for mirrors and may be used to find the height of the image or object or to find the magnification of a mirror.

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