# 1 32 Optical Images image formation reflection & refraction mirror & lens equations Human eye Spherical aberration Chromatic aberration

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• 32 Optical Imagesimage formationreflection & refractionmirror & lens equationsHuman eyeSpherical aberrationChromatic aberration

• image formationreal image: rays converge to a point Ex. suns rays focused by magnifier virtual image: apparent source of light divergence Ex. image seen in mirror

• Plane Mirror Imagedistances measured from mirror & axisimage height hi = object height hoobject distance do = image distance di

• *concave mirror images

• *convex mirror imagesalways virtual, upright, diminished

• *lens images

• *Lens & Mirror Equationrelate do, di & f.lateral magnification (LM) = hi/ho.you must learn the sign conventions to use these formulas

• imbedded objectimage distance < object distance

• *lens powerpower = 1/(focal-length(meters))unit: [D, diopters, 1/m]used for corrective lenses

Ex. near-sighted person P = -5.0D f = 1/P = 1/(-5) = -0.2m = -20cm.

• human eyeaverage index of refraction ~ 1.4

• Far Sighted Eyecorrection requires converging lens

• near sighted eyecorrection requires diverging lens

• Spherical AberrationSpherical aberration: light striking near edge focus at different points than light striking near center

• ChromaticAberrationChromatic aberration: different colors focus at different points

• SummaryImage formation by lenses & mirrorsReal/virtual, orientation, magnification.Near & far-sighted problem & correctionSpherical & chromatic aberration

• 2. A document is sealed in a glass cube (n=1.5) at a depth of 10cm from one surface. Calculate s and m. Object is in n1=1.5. Viewer is in air n2=1.00. Radius of surface is r = infinity.

1/s = -0.15 s = -6.67cm.

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• OI

• Question: Reverse the designations in the example above. Object is now the fish, so n1 = 1.33 (fish location). Let the fish be 10cm from bowl surface. Where is the image of the fish formed that the cat will see?Answer: s = 10cm , s = ?, r = -15cm, n1 = 1.33, n2 = 1.00.

0.133 + 1/s = 0.022 1/s = -0.111 s = -9.00cm

• Calculating Focal Length for a Thin LensExample: A double convex, thin glass lens with n = 1.5 has radii of curvature of 10 and 15cm. Find its focal length.

• s, cats nosen1 holds object, here equal to 1.000.1 +1.33/s= 0.022 1.33/s = -0.078 s = -17.1cm

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