1Find image with a thin lensFFfObjecthodohidiFFfObjecthodohidi2Analytical calculations Thin lens equation.fddoi111=+oioiddhhm −=≡:ionmagnificathohi3Analytical calculations Lens maker’s equation:The formula for a lens in vacuum (air):−−=211111RR)n(fn : index of refraction of the lens material.R1: radius of near surface. R2: radius of far surface. The near or far surface is with respect to the focal point FFFF. Near side is surface 1, far side is surface 2. The sign of the radius is then defined as “+” if the center is on the far side; “-” if the center is on the near side. In this convention, positive f means converging lens, negative f means diverging lens.FFFFnear surfacefar surface4Analytical calculations Lens maker’s equation:The formula for a lens (nlens) in medium nmedium:−−=211111RR)nn(fmediumlensR1: radius of near surface. R2: radius of far surface. FFFFnear surfacefar surfacenmedium5Sign convention table6Angular size The height of an object is measured by a meter stick. The height of the same object we see through our eyes depends on the how far away the object is to our eyes.7Angular size Angular size is defined to be: dh≡θ8Angular magnifying power Angular magnifying power: the ratio of the image angular size over the object angular size. 0θθ≡M9Human eyes The human eye is modeled in physics as a simple thin lens system with a fixed image distance, but the focal length can change in a range. di)(maxminf,ff∈10Human eyes The focal length range correspond to a person’s near point and far point: Near point: when the object is pushed as close as one can have clear image. This is the point when the eye’s focal lens is at its minimum value.11Human eyes The focal length range correspond to a person’s near point and far point: Far point: when the object is pushed as far as one can have clear image. Optically this is the point when the eye’s focal lens is at its maximum value. For healthy eyes, this far point is usually almost at infinity.12Vision corrections Nearsightedness (myopia):13Vision corrections Farsightedness (hyperopia):14Vision correction examples Refractive power: The reciprocal of the focal length. Often used by opticians and optometrists, who specify it in diopters (unit: 1/m). Nellie is nearsighted. She cannot focus on objects farther than 40.0 cm from her unaided eye. What focal length must her corrective contact lens have to bring into focus the most distant objects? fP1≡Far point = 40.0 cm, a correcting lens needs to generate the image of an object at infinity at this far point for her to see clearly. Contact lens means the correcting lens and the lens in the eye has zero distance between them.cm040.fc−=So the contact lens is a diverging lens with a focal length of -40.0 cm.15Vision correction examples Elizabeth is nearsighted. Without glasses, she can see objects clearly when they are between 15.0 cm and 90.0 cm away from her eyes. Her glasses are designed to be worn 2.00 cm from her eyes, and have a focal length so that objects at infinity produce images at her far point. When she is wearing these glasses, how close to her eye can an object be before it appears out of focus? Far point = 90.0 cm, near point = 15.0 cm. A correcting lens needs to generate the image of an object at infinity at this far point minus the 2.00 cm for her to see clearly. Contact lens means the correcting lens and the lens in the eye has zero distance between them.cm088.fc−=2.00 cmFar pointNear point = 15.0 cm. The image distance has to be -(15.0 – 2.0) cm = -13.0 cm of an object placed at the new near point with the correcting lens. Use the lens equation to find this new near point to be 15.25 cm.16Multiple lens system Microscope:Two lenses − objective and eyepieceObjective focal length very shortFirst image real, near eyepiece focal pointFinal image inverted, magnified, virtualAngular magnifying power is 0θθ0θθ≡M17The magnifying power of a microscopeeyeobeyeobffLNMMmM−≅=M = overall magnificationmob= objective lateral magnificationMey= eyepiece angular magnificationL = distance between the lensesN = near point distance of your eyefob= focal length of objectivefey= focal length of eyepiece18Multiple lens system TelescopeTwo converging lensesFocal points at same locationFinal image inverted, at infinity, virtualAngular magnifying power is 0θθ0θθ≡M19The magnifying power of a refracting telescopeeyeobobffM −=≡θθImage
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