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8. Thin lenses

Learn about thin lenses, including types, focus, main equations, and ray tracing for converging and diverging lenses. Explore examples of lenses and image formation scenarios.

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8. Thin lenses

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  1. 8. Thin lenses Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging or diverging. 1) Types of lenses • Example: An air bubble in a piece of glass has a double convex shape (see below). What type of the lens is formed? • Converging • Diverging • It depends on if nin > nout if nin > nout

  2. 2) Focus and focal plane A diverging lens make parallel light diverge. The focal point is that point where the diverging rays would converge if projected back. Parallel rays are brought to a focus by a converging lens.

  3. 3) Main equations Magnification Thin lens equation Lensmaker’s equation Note! We use different sign convention than in the Giancoli book Lens power: is measured in diopters, D. 1 D = 1 m-1 For mirrors and lenses we assume that the radius R is positive if the center is on the side of the outgoing (passing) rays, and that R is negative otherwise. R1>0 C2 C1 + R2<0 f < 0 f > 0

  4. 4) Ray tracing (thin converging lenses) f>0

  5. 4) Ray tracing (thin diverging lenses) f<0 4 2F 2F The image is upright and virtual Ray 1 leaves the top of the object and is drawn such that it is parallel to the axis; therefore it emerges from the lens along a line through the focal point on the back side of the lens. Ray 2 leaves the top of the object and is made to pass through the other focal point; therefore it emerges from the lens parallel to the axis. Ray 3 leaves the top of the object and is directed toward the very center of the lens; therefore it emerges from the lens a the same angle as it entered.

  6. converging lenses diverging lenses

  7. Example 1: The images formed by concave lenses • are always real • are always virtual • C) could be real or virtual; it depends on whether the object distance is smaller or greater than the focal length • D) could be real or virtual, but always real when the object is placed at the focal point Example 2: An object is placed between a convex lens and its focal point. The image formed is A) virtual and erect B) virtual and inverted C) real and erect D) real and inverted Example 3: A convex lens has a focal length f. An object is placed between f and 2f on the axis. The image formed is located A) at 2f B) between f and 2f C) at f D) at a distance greater than 2f from the lens

  8. Example 1: A thin symmetric lens provides an image of a fingerprint with a magnification +0.2 when the fingerprint is 1 cm farther from the lens than the focal point of the lens. What is the type of the image, and what is the type of the lens? Answer: Image is erect and virtual; this is diverging lenses Example 2: A glass converging lens has one flat side and another with a radius of 20 cm. What is the focal length of the lens? ( The index of refraction of the glass in the lens is 1.50)

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