11/13/2018. Lenses. Lenses. Light refracts at both surfaces. Non-parallel surfaces results in net bend.

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1 Light reracts at both suraces. Non-parallel suraces results in net bend. Focusing power o the lens is unction o radius o curvature o each surace and index o reraction o lens. Converging lenses are thicker in the center o the lens. Symmetric Thin Lens Approximation Assume all bend occurs along a line through the lens. Assume the same ocus on each side o the lens. Diverging lenses are thinner in the center o the lens. From the object to the lens, parallel to the principle axis From there (lens) through the ar ocal point From the object through the near ocal point to the lens rom there (lens) parallel to the principle axis

2 Calculation From the object through the center o the lens s + s' = m= y ' s ' y = s Object y Image 0or converging lens y ' s s ' Sign Conventions Positive associated with positive on opposite side o lens. Sign Conventions Negative associated with negative. Negative means near side ocal point is on ar side and ar side ocal point is on near side. 0 Example: A 3cm tall object is placed 2cm rom a converging thin lens with a ocal length o 8cm. (a) Where would the Example: A 3cm tall object is placed 2cm rom a converging thin lens with a ocal length o 8cm. (a) Where would the 2

3 Example: A 3cm tall object is placed 2cm rom a diverging thin lens with a ocal length o 8cm. (a) Where would the Example: A 3cm tall object is placed 2cm rom a diverging thin lens with a ocal length o 8cm. (a) Where would the Eyes and Corrective Lens causes light rays to converge on the back o the eye. Eyes and Corrective Focal length o human eye is adjustable. Muscles can pull lens, causing the lens to be thinner, less When muscles are relaxed, elasticity o lens restores lens to thicker shape, more Eyes and Corrective Focal length o human eye is adjustable. Muscles can pull lens, causing the lens to be thinner, less When muscles are relaxed, elasticity o lens restores lens to thicker shape, more The human eye eventually loses elasticity and loses some range in convergence, resulting in inability to ocus on near objects. Typically, there is signiicant loss between 40 and 50 years o age. Eyes and Corrective Some eyes have lenses that are too converging or not converging enough and need corrective lenses. Too converging Nearsighted Not converging enough Farsighted 3

4 Eyes and Corrective Some eyes have lenses that are too converging or not converging enough and need corrective lenses. Example: A student's natural lenses ocus light rom a distant object 0. cm in ront o the back o the eye. a. What kind o corrective lenses should the student use? b. What should be the ocal length o the corrective lenses? [The back o the human eye is ~2.4 cm rom the natural lens. Estimate the location o corrective lenses.] Too converging Nearsighted Corrected with diverging lens. Not converging enough Farsighted Corrected with converging lens. Example: A student's natural lenses ocus light rom a distant object 0. cm in ront o the back o the eye. a. What kind o corrective lenses should the student use? b. What should be the ocal length o the corrective lenses? [The back o the human eye is ~2.4 cm rom the natural lens. Estimate the location o corrective lenses.] Example: A student's natural lenses ocus light rom a distant object 0. cm in ront o the back o the eye. a. What kind o corrective lenses should the student use? b. What should be the ocal length o the corrective lenses? [The back o the human eye is ~2.4 cm rom the natural lens. Estimate the location o corrective lenses.] The image or the corrective lens will become the object or the natural lens. Determine the ocal length o the natural lens. The image or the corrective lens will become the object or the natural lens. Determine the ocal length o the natural lens. Determine an object distance or the natural lens that results in an image distance o 2.4 cm. Example: A student's natural lenses ocus light rom a distant object 0. cm in ront o the back o the eye. a. What kind o corrective lenses should the student use? b. What should be the ocal length o the corrective lenses? [The back o the human eye is ~2.4 cm rom the natural lens. Estimate the location o corrective lenses.] Example: A student's natural lenses ocus light rom a distant object 0. cm in ront o the back o the eye. a. What kind o corrective lenses should the student use? b. What should be the ocal length o the corrective lenses? [The back o the human eye is ~2.4 cm rom the natural lens. Estimate the location o corrective lenses.] The image or the corrective lens will become the object or the natural lens. Determine the ocal length o the natural lens. Determine an object distance or the natural lens that results in an image distance o 2.4 cm. Determine the image distance or the corrective lens. [The object or the natural lens is the image or the corrective lens, BUT the two distances are dierent because they are measured rom dierent lenses.] The image or the corrective lens will become the object or the natural lens. Determine the ocal length o the natural lens. Determine an object distance or the natural lens that results in an image distance o 2.4 cm. Determine the image distance or the corrective lens. Determine the ocal length or the corrective lens. 4

5 More Complex Lensmaker s Equation Reraction at Spherical Suraces 0 Object 0 0or converging 0or diverging (Surace is irst surace hit by light.) Reraction at Spherical Suraces Reraction at Spherical Suraces Reraction at Spherical Suraces Reraction at Spherical Suraces Calculations (or ) (Note that ) 5